⚖️ 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
Enter coefficients for ax² + bx + c = 0
Solution Formulas
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.
Related Calculators
Quadratic Formula Calculator
Solve quadratic equations ax² + bx + c = 0 using the quadratic formula.
Algebra Calculator
Solve algebraic expressions and evaluate equations step by step.
Polynomial Calculator
Add, subtract, and multiply polynomials. Evaluate polynomials at given values.