How to Calculate Cubic Equation Solver

What is Cubic Equation Solver?

A cubic equation has the form ax³ + bx² + cx + d = 0 and always has three roots (which may be real or complex, and some may be repeated). Cardano's formula (1545) was the first general algebraic solution for cubics, though numerical methods are used in practice.

Formula

Depress the cubic: substitute x = t − b/(3a) to eliminate the x² term

x: t − b/(3a) to eliminate the x² term — t − b/(3a) to eliminate the x² term

Step-by-Step Guide

1Depress the cubic: substitute x = t − b/(3a) to eliminate the x² term
2Solve the depressed form t³ + pt + q = 0 using Cardano's formula
3Three real roots occur when the discriminant Δ = −4p³ − 27q² > 0
4One real root when Δ < 0, three roots (one repeated) when Δ = 0

Worked Examples

Input

x³ − 6x² + 11x − 6 = 0

Result

x = 1, 2, 3

Three distinct integer roots — verify: (x−1)(x−2)(x−3)

Input

x³ − 3x + 2 = 0

Result

x = 1 (double root), x = −2

Δ = 0 indicates a repeated root

Frequently Asked Questions

What is Cubic Equation?

A cubic equation has the form ax³ + bx² + cx + d = 0 and always has three roots (which may be real or complex, and some may be repeated). Cardano\

How accurate is the Cubic Equation calculator?

The calculator uses the standard published formula for cubic equation. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.

What units does the Cubic Equation calculator use?

This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.

What formula does the Cubic Equation calculator use?

The core formula is: Depress the cubic: substitute x = t − b/(3a) to eliminate the x² term. Each step in the calculation is shown so you can verify the result manually.

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