Cubic Equation

from math import sqrt, acos, cos, pi

# Coefficients of x^3 + (C_1)x^2 + (C_2)x + C_3 = 0
C = [1,   # Coefficient C_1
     1,                       # Coefficient C_2
     1               # Coefficient C_3
    ]
# Substitutions (see solution of Cubic equations:
#                         mathworld.wolfram.com/CubicFormula.html )
w = (3*C[1] - C[0]**2)/3.0
q = (27*C[2] - 9*C[0]*C[1] + 2*C[0]**3)/27.0
R_t = (w/3.0)**3 + (q/3.0)**2.0
q_s = q/abs(q) #math.copysign(1, q)

if  R_t < 0:
    Ratio = sqrt(((q/2.0)**2)/(-(w/3.0)**3))
    if abs(Ratio) < 1.0:
        phi = acos(Ratio)
    else:
        raise ValueError # Raise Math error if no solution
        #phi = math.degrees(math.acos(Ratio-2)+math.pi)
             # math.degrees(math.acos(Ratio-2))
else:
    raise ValueError  # Add this to your exception handling for when a solution does not exist.
# Analytical expressions for roots:
roots = [-2*q_s*sqrt(-w/3.0)*cos(phi/3.0           ) - C[0]/3.0,
         -2*q_s*sqrt(-w/3.0)*cos(phi/3.0 + 2*pi/3.0) - C[0]/3.0,
          2*q_s*sqrt(-w/3.0)*cos(phi/3.0 + 4*pi/3.0) - C[0]/3.0
          ]