Polynomial equation

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) + D^1/2 ] ^1/3
v = [ (-q/2) – D^1/2 ] ^1/3
x = u+v
s = [- (u+v)/2 ]
t = [(u-v / 2) * 3^1/2]
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 ]

• 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