Discriminant and Cubic Root Formula - Polynomial Equation Solver

Formula:

p = (1/3) [(3c/a) - (b2) / a2) ]
q = (1/27) [ (2b3 / a3) - (9bc / a2) + (27e / a) ]
D = (p/3)3 + (q/2)2

If D value is greater than 0:

u = [ (-q/2) + D1/2 ] 1/3
v = [ (-q/2) - D1/2 ] 1/3
x = u+v
s = [- (u+v)/2 ]
t = [(u-v / 2) * 31/2]
y = s+t
z = s-t

If D value is less than 0:

Φ = acos [ (-q/2) (|p| / 3) -3/2 ]
x = 2 [ (|p| / 3)1/2 cos (Φ/3) ]
y = -2 [ (|p| / 3)1/2 cos (Φ + π)/3 ]
z =-2 [ (|p| / 3)1/2 cos (Φ - π)/3 ]


Where,
D = Discriminant
p,q = Real Constant
a,b,c,e = Real Constant
x,y,z = Cubic root
u,v = Real Constant
s,t = Temp Variable
cos = Cosine
Φ = Angle

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