Quadratic Equation Solver (Lua)

-- Quadratic equation solver
-- (C) Linus Ramneborg 2018
-- All rights reserved. No redistribution allowed.

-- Description:
-- Function used to solve for x1, x2 with numbers from a
-- quadtratic equation, a so-called PQ formula.
-- p represents p in px + q = 0, q represents q in that formula. You get it.
-- The 'swap' variable is there so you can swap from + to - when calculating.
-- https://en.wikipedia.org/wiki/Quadratic_equation

function pq(p,q, swap)
  if p < 0 then error("bad argument #1, negative number not possible") end
  if type(q) == "number" and q < 0 then error("bad argument #2, negative number not possible") end
  if not swap then swap = false end

  local x1, x2 = 0
  -- Calculate x1, x2 using x^2 + px + q = 0 solution
  if not swap then
    -- Check if q is a variable present
    if q then
      x1 = -(p/2) + (((p/2)^2)+q)^0.5

      x2 = -(p/2) - (((p/2)^2)+q)^0.5
    else
      x1 = -(p/2) + (((p/2)^2))^0.5

      x2 = -(p/2) - (((p/2)^2))^0.5
    end
  else
    -- Check if q is a variable present
    if q then
      x1 = -(p/2) + (((p/2)^2)-q)^0.5

      x2 = -(p/2) - (((p/2)^2)-q)^0.5
    else
      x1 = -(p/2) + (((p/2)^2))^0.5

      x2 = -(p/2) - (((p/2)^2))^0.5
    end

  end

  return x1, x2

end