Cubic Equation Solver

Cubic equations model cubic volume optimizations, thermodynamic equations of state (such as Van der Waals gas laws), and structural deflection curves under non-uniform beam loading.

This calculator computes all 3 roots of any third-degree polynomial with real coefficients, classifying whether the roots are three distinct real numbers, repeated real numbers, or one real root accompanied by two complex conjugate roots.

The polynomial is depressed to t³ + pt + q = 0 by substituting x = t - b/(3a). Cardano's discriminant Δ = (q/2)² + (p/3)³ determines the nature of the roots via trigonometric or hyperbolic solutions.