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The Cubic Equation has the form ax³ + bx² + cx + d = 0. It must have the term in x³ or it would not be cubic but any or all of b, c and d can be zero.

Cubic Equation calculator formula

x₁=(- term1 + r₁₃*cos(q³/3) )
x₂=(- term1 + r₁₃*cos(q³+(2*∏)/3) )
x₃=(- term1 + r₁₃*cos(q³+(4*∏)/3) )

Where: discriminant(Δ) = q³ + r²
q = (3c- b²)/9
r = -27d + b(9c-2b²)
s = r + √(discriminant)
t = r - √(discriminant)
term1 = √(3.0)*((-t + s)/2)
r₁₃= 2 * √(q)

Enter values for a, b, c and d get the result x.

For example: a=1, b=8, c=16 and d=10,
x₁ = -5.365230013414097
x₂ = -1.3173849932929516 + 0.3582593599240431 i
x₃ = -1.3173849932929516 - 0.3582593599240431 i