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⚖️ Equation Solver

Solve linear equations (ax + b = c) or quadratic equations (ax² + bx + c = 0) with full step-by-step solutions. Handles real and complex roots automatically.

Enter coefficients for ax + b = c

x +
=

Solution Formulas

Linear: ax + b = c  →  x = (c − b) / a
Quadratic: x = (−b ± √(b²−4ac)) / (2a)
Discriminant: Δ = b² − 4ac  (determines root type)

Frequently Asked Questions

A linear equation is one where the variable (x) appears only to the first power, like 2x + 5 = 13. The graph of a linear equation is always a straight line.

The discriminant is b² − 4ac in a quadratic equation. It tells you how many real roots exist: Δ > 0 means two distinct real roots, Δ = 0 means one repeated real root, and Δ < 0 means two complex (imaginary) roots.

Real roots are ordinary numbers. Complex (imaginary) roots occur when Δ < 0 and involve √(−1) = i. They always appear in conjugate pairs (a + bi and a − bi) for equations with real coefficients.

Substitute the solution back into the original equation. For ax + b = c: compute a(x) + b and verify it equals c. For quadratics: compute ax² + bx + c and verify it equals 0.

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