📉 Cubic Equation Solver
Solve a cubic equation in the form ax³ + bx² + cx + d = 0 and get all three roots.
What this calculator solves
This calculator finds the roots of a cubic equation in the standard form ax³ + bx² + cx + d = 0. A cubic equation always has three roots (counting repeats), which may be three real numbers, or one real number plus a pair of complex conjugate numbers.
The method used
The equation is first converted to a depressed cubic (removing the squared term), then solved with Cardano’s formula. A discriminant value determines the type of roots: a positive discriminant gives one real root and a complex conjugate pair, a discriminant near zero gives a repeated real root, and a negative discriminant gives three distinct real roots (found using a trigonometric form of Cardano’s method).
This tool is intended for general math and engineering learning purposes. Results are rounded and may show small floating-point rounding differences.