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Cubic Equation Calculator

Solve cubic equations ax³ + bx² + cx + d = 0 for all three roots (real and complex) with the discriminant.

Enter values

Results update as you type.

Result

Roots

1, 2, 3

Discriminant Δ
4
Real roots
3
Factored form
(x - 1)(x - 2)(x - 3)

About the Cubic Equation Calculator

Solve cubic equations ax³ + bx² + cx + d = 0 for all three roots (real and complex) with the discriminant.

Also known as: cubic solver, third degree equation, solve cubic, cubic roots.

How to use this calculator

  1. Enter a, b, c, d.
  2. The result updates instantly as you type — press Calculate (or Enter) at any time.
  3. Review the breakdown shown under the main result.
  4. Use Copy result or Share to save the answer or send a link with your inputs.

Formula

Δ = 18abcd − 4b³d + b²c² − 4ac³ − 27a²d²

Worked example

Using the values pre-filled in the calculator above:

  • a = 1
  • b = -6
  • c = 11
  • d = -6

the calculator returns:

  • Roots: 1, 2, 3
  • Discriminant Δ: 4
  • Real roots: 3
  • Factored form: (x - 1)(x - 2)(x - 3)