import math
import cmath
def input_coef(): #ввод данных
    print("Введите коэффициенты:")
    a=float(input("a="))
    b=float(input("b="))
    c=float(input("c="))
    d=float(input("d="))
    return a,b,c,d

def check(coef): #проверка, что уравнение кубическое
    a=float(coef[0])
    b=float(coef[1])
    c=float(coef[2])
    d=float(coef[3])
    print ("Заданы коэффициенты:", a, b, c, d)
    if abs(a) > 1e-6:
        return a, b, c, d
    else:
        return False

def Vieta(coef): #решение уравнения
    print("Решение кубического уравнения Ax^3 + Bx^2 + Cx + D = 0")
print("Тригонометрической формулой Виета")
k_a = a
k_b = b
k_c = c
k_d = d
a = k_b / k_a
b = k_c / k_a
c = k_d / k_a
q = (a**2 - 3 * b) / 9
r = (2 * a**3 - 9 * a * b + 27 * c) / 54
s = q**3 - r**2
if s > 0:
    from math import acos, cos, sqrt, pi
    f = (1 / 3) * acos(r / sqrt(q**3))
    x1 = -2 * sqrt(q) * cos(f) - (a / 3)
    x2 = -2 * sqrt(q) * cos(f + (2 / 3) * pi) - (a / 3)
    x3 = -2 * sqrt(q) * cos(f - (2 / 3) * pi) - (a / 3)
    print("Q = ", q)
    print("R = ", r)
    print("S = ", s)
    print("fi = ", f)
    print("x1 = ", x1)
    print("x2 = ", x2)
    print("x3 = ", x3)
elif s < 0:
    if q > 0:
        from cmath import acosh, cosh, sinh, sqrt
        f = (1 / 3) * acosh((abs(r)) / (sqrt(q**3)))
        if r > 0:
            x1 = -2 * sqrt(q) * cosh(f) - (a / 3)
            x2 = sqrt(q) * cosh(f) - (a / 3) + 1j * sqrt(3) * sqrt(q) * sinh(f)
            x3 = sqrt(q) * cosh(f) + (a / 3) + 1j * sqrt(3) * sqrt(q) * sinh(f)
            print("Q = ", q)
            print("R = ", r)
            print("S = ", s)
            print("fi = ", f)
            print("x1 = ", x1)
            print("x2 = ", x2)
            print("x3 = ", x3)
        elif r == 0:
            x1 = -a / 3
            x2 = (-a / 3) - 1j * sqrt(3) * sqrt(q) * sinh(f)
            x3 = (-a / 3) + 1j * sqrt(3) * sqrt(q) * sinh(f)
            print("Q = ", q)
            print("R = ", r)
            print("S = ", s)
            print("fi = ", f)
            print("x1 = ", x1)
            print("x2 = ", x2)
            print("x3 = ", x3)
        else:
            x1 = 2 * sqrt(q) * cosh(f) - a / 3
            x2 = -1 * sqrt(q) * cosh(f) - a / 3 + 1j * sqrt(3) * sqrt(q) * sinh(f)
            x3 = -1 * sqrt(q) * cosh(f) - a / 3 - 1j * sqrt(3) * sqrt(q) * sinh(f)
            print("Q = ", q)
            print("R = ", r)
            print("S = ", s)
            print("fi = ", f)
            print("x1 = ", x1)
            print("x2 = ", x2)
            print("x3 = ", x3)
    elif q < 0:
        from cmath import asinh, cosh, sinh, sqrt
        f = (1 / 3) * asinh(abs(r) / sqrt(q**3))
        if r > 0:
            x1 = -2 * sqrt(abs(q)) * sinh(f) - a / 3
            x2 = sqrt(abs(q)) * sinh(f) - a / 3  + 1j * sqrt(3) * sqrt(abs(q)) * cosh(f)
            x3 = sqrt(abs(q)) * sinh(f) - a / 3  - 1j * sqrt(3) * sqrt(abs(q)) * cosh(f)
            print("Q = ", q)
            print("R = ", r)
            print("S = ", s)
            print("fi = ", f)
            print("x1 = ", x1)
            print("x2 = ", x2)
            print("x3 = ", x3)
        elif r == 0:
            x1 = -a / 3
            x2 = -a / 3 + 1j * sqrt(3) * sqrt(abs(q)) * cosh(f)
            x3 = -a / 3 - 1j * sqrt(3) * sqrt(abs(q)) * cosh(f)
            print("Q = ", q)
            print("R = ", r)
            print("S = ", s)
            print("fi = ", f)
            print("x1 = ", x1)
            print("x2 = ", x2)
            print("x3 = ", x3)
        else:
            x1 = 2 * sqrt(abs(q)) * sinh(f) - a / 3
            x2 = -1 * sqrt(abs(q)) * sinh(f) - a / 3 + 1j * sqrt(3) * cosh(f)
            x3 = -1 * sqrt(abs(q)) * sinh(f) + a / 3 + 1j * sqrt(3) * cosh(f)
            print("Q: = ", q)
            print("R = ", r)
            print("S = ", s)
            print("fi = ", f)
            print("x1 = ", x1)
            print("x2 = ", x2)
            print("x3 = ", x3)
    else:
        from cmath import sqrt
        x1 = -((c - (a * 3) / 27))**(1 / 3) - a / 3
        x2 = (-a + x1) / 2 + 1j / 2 * sqrt(abs((a - 3 * x1) * (a + x1) - 4 * b))
        x3 = x2 = (-a + x1) / 2 - 1j / 2 * sqrt(abs((a - 3 * x1) * (a + x1) - 4 * b))
        print("Q = ", q)
        print("R = ", r)
        print("S = ", s)
        print("fi = ", f)
        print("x1 = ", x1)
        print("x2 = ", x2)
        print("x3 = ", x3)
else:
    x1 = -2 * (r)**(1 / 3) - a / 3
    x2 = (r)**(1 / 3) - a / 3
    print("Q = ", q)
    print("R = ", r)
    print("S = ", s)
    print("fi = ", f)
    print("x1 = ", x1)
    print("x2 = ", x2)

    return  x1, x2, x3


coef = input_coef()
check = check(coef)
if check != False:
    roots = Vieta(coef)

else:
    print("Уравнение не кубическое")