Cubic Equation Solver
Solve cubic equations ax³ + bx² + cx + d = 0 with Cardano's method
Cubic Equation Form: \(ax^3 + bx^2 + cx + d = 0\)
Results
Enter values and click Calculate to see the result.
Theory & Formula
Theory
A cubic equation is a polynomial equation of degree three
Discriminant
\(\Delta = -4p^3 - 27q^2\)
- • When Δ > 0: Three distinct real roots
- • When Δ = 0: At least two roots are equal
- • When Δ < 0: One real and two complex conjugate roots
Cardano's Formula
Cardano's formula (named after Gerolamo Cardano, 16th century) provides algebraic solutions
Example
Solve x³ - 6x² + 11x - 6 = 0
\(x^3 - 6x^2 + 11x - 6 = 0\)
Solution: x₁ = 1, x₂ = 2, x₃ = 3 (three distinct real roots)