Can it solve equations with complex roots?

Yes — for quadratic equations with a negative discriminant the two complex conjugate roots are displayed in a + bi form.

How does the cubic solver work?

It uses Newton-Raphson numerical iteration to find up to three real roots, deflating the polynomial after each root is found.

When are results shown as fractions?

When a root is a rational number (detected via GCD), it is displayed as a simplified fraction alongside its decimal approximation.

What if the system of equations has no solution?

If the determinant is zero the solver reports that the system is either inconsistent (no solution) or dependent (infinite solutions).

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Equation Solver

Solve linear, quadratic, cubic, and simultaneous equations with step-by-step working.

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About this tool

Enter coefficients and the solver handles four equation types: single-variable linear (ax + b = c), quadratic (ax² + bx + c = 0) with real and complex roots, a 2×2 system of linear equations via Cramer's rule, and cubic (ax³ + bx² + cx + d = 0) using Newton-Raphson iteration. Every solution includes step-by-step working, and rational roots are displayed as fractions.

How to use

1 Select the equation type using the tab buttons at the top.
2 Enter the required coefficients in the input fields shown.
3 Click 'Solve' to calculate the solution.
4 Read the step-by-step working shown below the result to understand the method used.

Frequently Asked Questions

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