Cubic Equation Calculator

Cubic Equation Calculator

Solve cubic equations of the form ax³ + bx² + cx + d = 0 using Cardano's method.

Last updated: June 2026 | By Patchworkr Team

Cubic Solver

Equation

1-6+ 11x -6 = 0

Roots

Press Solve to calculate the roots.

What does Cardano's method do?

It converts the cubic into a depressed cubic and uses the discriminant to determine how many real and complex roots appear.

How to Use It

  1. Enter coefficients a, b, c, and d.
  2. Press Solve to compute the roots.
  3. Check the discriminant and root list on the right.

Can a be zero?

No. If a is zero, the equation is not cubic.

Can the roots be complex?

Yes. Cubic equations can have one real root and two complex conjugate roots.

Does the calculator accept decimals?

Yes. It accepts finite decimals and scientific notation.

Why show the discriminant?

It helps you understand whether the equation has repeated or distinct roots.

Formula Notes

Normalize by dividing by a, then use Q and R.
Discriminant: Δ = Q³ + R²

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