print("\n———————————————————————————————————————————————\n")
print("       Квадратные уравнения    versa 1.1          ")
print("                  by soviet~                    ")
print(" ")
print("        БУДЬТЕ ОСТОРОЖНЫ И НЕ ПАЛИТЕСЬ")
print("                 good luck))0")
print(" ")
print("\n———————————————————————————————————————————————\n")

function math.eval(eval)
   return assert(loadstring('return "" .. ' .. eval)) ();
end

function math.isFloat(int)
   return int ~= math.floor(int)
end

function math.isInt(int)
   return int == math.floor(int)
end

function math.detectNumbers(flt)
   flt = tostring(flt)
   if(string.find(flt, "%.")) then
      return string.len(string.gsub(flt, "[%d]+%.", ""))
   else
      return 0
   end
end

function math.removeAfter(flt)
   flt = tostring(flt)
   return string.gsub(flt, "%.[%d]+", "");
end

function math.nod(a,b,...)
   if b == nil then return a end
   while a ~= 0 and b ~= 0 do
      if a > b then
         a = a % b
      else
         b = b % a
      end
   end
   return math.nod(a + b,...)
end

function math.onlyDigits(num, numDecimalPlaces)
   local mult = 10^(numDecimalPlaces or 0)
   return math.floor(num * mult + 0.5) / mult
end

function math.equalOffset(x, y)

   return x > y - 0.0000003 and x < y + 0.0000003

end

function math.findCommon(num, onlyNum, addition)

   if(math.isInt(num)) then

      if(onlyNum) then

         return num;

      else

         return "\n" .. addition .. num;

      end

   end

   local oldNum = num;

   local smesh = false;

   local znam = 10^math.detectNumbers(num);

   local chisl = num * znam;

   local celoe = 0;

   local isNegative = "+";

   if(tonumber(num) < 0) then isNegative = "-";  chisl = math.abs(chisl); znam = math.abs(znam); oldNum = math.abs(oldNum) end

   if(chisl > znam) then

      celoe = math.floor(chisl/znam)

      chisl = math.fmod(chisl,znam)

      oldNum = oldNum - math.floor(oldNum)

      if(chisl == znam or chisl == 0) then

         smesh = true;

      end

   end

   local foundNeed = false;

   for x = 2,100 do

      for y = 1,100 do

         if(math.equalOffset(y*math.sqrt(x), oldNum)) then

            if(not onlyNum) then

               print(addition .. y .. "√" .. x)

            end

            break;

         end

         if(foundNeed) then break; end

      end

   end

   for x = 0,10000 do

      for y = 0,10000 do

         if(math.equalOffset(x/y, oldNum)) then

            chisl = x

            znam = y

            foundNeed = true;

            break;

         end

         if(foundNeed) then break; end

      end

   end

   local nod = math.nod(chisl, znam)

   if(nod and nod > 1) then

      znam = znam / nod;

      chisl = chisl / nod;

   end

   if((math.isInt(chisl) and math.isInt(znam)) or smesh or true) then

      if(smesh) then

         if(onlyNum) then

            return isNegative .. " " .. celoe;

         else

            return addition .. isNegative .. " " .. celoe;

         end

      else

         local tires = "";

         for i=1,string.len(znam) do

            tires = tires .. "—";

         end

         if(celoe > 0) then

            local spaces = "";

            for i=1,string.len(celoe) do

               spaces = spaces .. " ";

            end

            if(onlyNum) then

               return isNegative .. math.removeAfter(celoe) .. " " .. isNegative .. " ( " .. math.removeAfter(chisl) .. " / " .. math.removeAfter(znam) .. " )"

            else

               return "\n          " .. spaces .. math.removeAfter(chisl) .. "\n" .. addition .. isNegative .. " " .. math.removeAfter(celoe) .. " ——" .. tires .. "\n           " .. spaces .. math.removeAfter(znam) .. "\n\n" .. "\n" .. addition .. num

            end

         else

            if(onlyNum) then

               return isNegative .. " ( " .. math.removeAfter(chisl) .. " / " .. math.removeAfter(znam) .. " )"

            else

               return "\n          " .. math.removeAfter(chisl) .. "\n" .. addition .. isNegative .. " ——" .. tires .. "\n          " .. math.removeAfter(znam) .. "\n\n" .. "\n" .. addition .. num;

            end

         end

      end

   else

      if(onlyNum) then

         return num;

      else

         return "\n" .. addition .. num;

      end

   end

end

function round(num, numDecimalPlaces)
   if numDecimalPlaces and numDecimalPlaces>0 then
      local mult = 10^numDecimalPlaces
      return math.floor(num * mult + 0.5) / mult
   end
   return math.floor(num + 0.5)
end

repeat

   print("  Теперь вводим a:\n")
   a = io.read()
   print("  Теперь вводим b:\n")
   b = io.read()
   print("  Теперь вводим c:\n")
   c = io.read()
   D = (b*b) - (4*a*c)
   print("\n———————————————————————————————————————————————\n")
   print("  Способ 1.")
   print("\n———————————————————————————————————————————————\n")
   print("\n     ФОРМУЛЫ\n")
   print("\n  D = b² - 4ac\n")

   sqrtOld = math.sqrt(math.abs(D))

   if(math.isFloat(sqrtOld)) then sqrt = math.findCommon(sqrtOld, true) end;

   if(D > 0) then
      print("\n        -b - √D")
      print("  x1 = —————————")
      print("          2a\n")
      print("        -b + √D")
      print("  x2 = —————————")
      print("          2a")
      x1 = ((b*-1)-sqrtOld)/(2*a)
      x2 = ((b*-1)+sqrtOld)/(2*a)
      print("\n\n     РЕШЕНИЕ\n\n")
      print("  D = " .. b .. "² - 4*" .. a .. "*" .. c)
      print("  D = " .. b*b .. " - " .. 4*a*c)
      print("\n  D = " .. D)
      print("\n       " .. b*-1 .. " - √" .. D)
      print("  x1 = ————————————————————")
      if(a == 1) then
         print("          " .. a)
      else
         print("        2 * " .. a)
      end
      print("\n        " .. b*-1 .. " - " .. sqrtOld)
      print("  x1 = ————————————————————")
      print("        " .. 2*a)
      print(math.findCommon(x1, false, "  x1 = "))
      print("\n\n        " .. b*-1 .. " + √" .. D)
      print("  x2 = ————————————————————")
      if(a == 1) then
         print("          " .. a)
      else
         print("        2 * " .. a)
      end
      print("\n       " .. b*-1 .. " + " .. sqrtOld)
      print("  x2 = ————————————————————")
      print("        " .. 2*a)
      print(math.findCommon(x2, false, "  x2 = "))
      print("\n\n ОТВЕТ: " .. math.findCommon(x1, true) .. "; " .. math.findCommon(x2, true))

      print("\n———————————————————————————————————————————————\n")
      print("  Способ 2.")
      print("\n———————————————————————————————————————————————\n")
      print("\n     ФОРМУЛЫ\n")
      x1 = (b/2)*-1+math.sqrt(math.abs((b/2)^2-c))
      x2 = (b/2)*-1-math.sqrt(math.abs((b/2)^2-c))
      print("\n          p")
      print("  x1 = - ——— + √(p/2)²-q")
      print("          2\n")
      print("\n          p")
      print("  x2 = - ——— - √(p/2)²-q")
      print("          2\n")
      print("\n\n     РЕШЕНИЕ\n\n")
      print("\n          " .. b)
      print("  x1 = - ——— - √(" .. b .. "/2)²-" .. c)
      print("          2")
      print("\n  x1 = " .. b/2*-1 .. " - √(" .. b/2 .. ")²-" .. c)
      print(math.findCommon(x1, false, "  x1 = "))
      print("\n          " .. b)
      print("  x2 = - ——— + √(" .. b .. "/2)²-" .. c)
      print("          2")
      print("\n  x2 = " .. b/2*-1 .. " + √(" .. b/2 .. ")²-" .. c)
      print(math.findCommon(x2, false, "  x2 = "))
      print("\n\n ОТВЕТ: " .. math.findCommon(x1, true) .. "; " .. math.findCommon(x2, true))

      if(math.fmod(b, 2) == 0) then

         print("\n———————————————————————————————————————————————\n")
         print("  Способ 3.")
         print("\n———————————————————————————————————————————————\n")
         print("\n     ФОРМУЛЫ\n")
         k = b/2
         x1 = ((k*-1)+math.sqrt(k^2-a*c))/a;
         x2 = ((k*-1)-math.sqrt(k^2-a*c))/a;
         print("\n       -k+√(k²-ac)")
         print("  x1 = ————————")
         print("        a\n")
         print("\n       -k-√(k²-ac)")
         print("  x2 = ————————")
         print("        a\n")
         print("\n\n     РЕШЕНИЕ\n\n")
         print("\n       " .. k*-1 .. " + √(" .. k .. "²-" .. a .. "*" .. c .. ")")
         print("  x1 = ———————————")
         print("        " .. a .. "\n")
         print("\n  x1 = ( " .. k*-1 .. " + √ ( " .. k^2 .. " - " .. a*c .. " ) ) / " .. a)
         print(math.findCommon(x1, false, "  x1 = "))
         print("\n       " .. k*-1 .. " - √(" .. k .. "²-" .. a .. "*" .. c .. ")")
         print("  x2 = ———————————")
         print("        " .. a .. "\n")
         print("\n  x2 = ( " .. k*-1 .. " - √ ( " .. k^2 .. " - " .. a*c .. " ) ) / " .. a)
         print(math.findCommon(x2, false, "  x2 = "))
         print("\n\n ОТВЕТ: " .. math.findCommon(x1, true) .. "; " .. math.findCommon(x2, true))

      end

   elseif(D < 0) then
      print("\n\n     РЕШЕНИЕ\n\n")
      print("  D = " .. b .. "² - 4*" .. a .. "*" .. c)
      print("  D = " .. b*b .. " - " .. 4*a*c)
      print("\n  D = " .. D)
      print("\n\n   корней нет.")
      print("\n\n ОТВЕТ: корней нет.")
   elseif(D == 0) then
      print("\n        -b")
      print("  x = ———————")
      print("        2a\n")
      print("\n\n     РЕШЕНИЕ\n\n")
      print("  D = " .. b .. "² - 4*" .. a .. "*" .. c)
      print("  D = " .. b*b .. " - " .. 4*a*c)
      print("\n  D = " .. D)
      print("\n       " .. b*-1)
      print("  x = ————————————")
      if(a == 1) then
         print("          " .. a)
      else
         print("        2 * " .. a)
      end
      x = round((b*-1)/(2*a), 3)
      print("\n  x = " .. math.findCommon(x, true))
      print("\n\n ОТВЕТ: " .. math.findCommon(x, true))
      --print("          " .. b*-1 .. "\nx = —————————————————— = " .. x .. " \n           " .. 2*a .. "\n")
   end
   print("\n———————————————————————————————————————————————\n\n\n")

until 0 == 1