Solve any cubic equation instantly with our advanced cubic equation solver calculator. Get step-by-step solutions, find all real and complex roots, and visualize the cubic function graph.
Must be non-zero (required for cubic equation)
A cubic equation is a polynomial equation of degree three, written in the standard form ax³ + bx² + cx + d = 0, where a, b, c, and d are constants, and a ≠ 0. Our cubic equation solver handles all types of cubic equations, from simple forms like x³ - 8 = 0 to complex equations with all coefficients present.
When the discriminant is positive, the cubic equation has three distinct real roots. Our calculator shows all three solutions with exact forms when possible.
When the discriminant is negative, there's one real root and a pair of complex conjugate roots. Perfect for advanced mathematics and engineering applications.
When the discriminant equals zero, the equation has multiple roots. This could be a triple root or a double root with another single root.
Our cubic equation solver uses Cardano's method, a powerful mathematical technique discovered in the 16th century. This algorithm handles all cases of cubic equations, providing exact solutions when possible and numerical approximations for complex cases. The calculator automatically determines the best approach based on your equation's coefficients.
Our calculator provides solutions accurate to at least 10 decimal places for numerical results and exact forms when applicable to rational roots.
Yes! Our cubic equation solver accepts fractional, decimal, and integer coefficients, making it perfect for all types of mathematical problems.
Real roots are numbers that exist on the number line, while complex roots involve imaginary numbers (i = √-1). Complex roots always come in conjugate pairs.
Simply plug each root back into the original equation. If the result equals zero, the root is correct. Our calculator can also help you verify solutions.