Online Equation Solver
Solve linear and quadratic equations instantly. Get step-by-step solutions, discriminant analysis, and exact or decimal roots for your algebra problems.
Solve Your Equations
Select the type of equation, input the coefficients, and receive a detailed, step-by-step mathematical breakdown of the solution.
Equation Parameters
Define your mathematical expression
Solution Evaluation
Step-by-step mathematical breakdown
Standard Algebraic Forms
Fundamental formulas and rules used by the equation solver to compute accurate results.
| Equation Type | Standard Form | Solution Formula |
|---|---|---|
| Linear | ax + b = 0 | x = -b / a |
| Quadratic | ax² + bx + c = 0 | x = (-b ± √(b² – 4ac)) / 2a |
| Discriminant (Δ) | Δ = b² – 4ac | Determines root nature (Real or Complex) |
| Sum of Roots | x₁ + x₂ | -b / a |
| Product of Roots | x₁ × x₂ | c / a |
Equation Solving FAQ
Everything you need to know about solving linear and quadratic equations.
A quadratic equation is a second-degree polynomial equation in a single variable x, with the standard form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
The discriminant is the part of the quadratic formula under the square root: Δ = b² – 4ac. It determines the nature of the roots: if positive, there are two distinct real roots; if zero, there is exactly one real root (a repeated root); if negative, there are two complex conjugate roots.
Yes. If the discriminant is negative, the calculator will automatically compute and display the complex roots in the standard mathematical format: a + bi, where ‘i’ is the imaginary unit (√-1).
If ‘a’ is zero in a quadratic equation, it ceases to be quadratic and becomes a linear equation (bx + c = 0). The solver will detect this and either prompt you to adjust the inputs or solve it as a linear equation, provided b ≠ 0.