Cubic Equation Solver

Solve cubic equations ax³+bx²+cx+d=0. Free online cubic equation calculator.

The Cubic Equation Solver finds all roots of cubic equations in the form ax³ + bx² + cx + d = 0. Using Cardano's formula and numerical methods, this calculator handles all cases including one real root and two complex roots, or three real roots. Enter your coefficients to find all solutions.

Common use cases

  • Engineering design problems
  • Physics applications
  • Optimization problems
  • Advanced algebra coursework
  • Mathematical modeling

How to use

  1. Enter coefficient a (x³ term)
  2. Enter coefficient b (x² term)
  3. Enter coefficient c (x term)
  4. Enter coefficient d (constant)
  5. Click solve for all roots

FAQ

How many roots does a cubic have?

Always exactly 3 roots (counting multiplicity and complex roots). Either 3 real or 1 real + 2 complex conjugates.

What is Cardano's formula?

An algebraic method for solving cubics, similar to but more complex than the quadratic formula.

Can I solve x³ = 8?

Yes, enter a=1, b=0, c=0, d=-8. Solutions: x=2, x=-1±i√3.

What about higher degree polynomials?

Use our quartic solver for degree 4, or polynomial root finder for higher degrees.