Equation Solver: The Complete Guide
Solve linear and quadratic equations instantly. Enter the coefficients a, b, and c for ax² + bx + c = 0 to find the roots — real or complex — or a linear solution when a is zero.
Who the Equation Solver is for
Students solving quadratic and linear equations who want exact roots and the discriminant.
How to use the Equation Solver
- Type your values into the fields above — pick your currency or units where the calculator offers them.
- Results update automatically as you type; there's no submit button and nothing is sent to a server.
- Adjust any input to compare scenarios, then copy the result with a single click.
How it works
For ax² + bx + c = 0, the roots are x = (−b ± √(b² − 4ac)) ÷ 2a. The discriminant b² − 4ac decides whether there are two real, one repeated, or two complex roots. If a = 0, it solves the linear equation bx + c = 0.
Features
- Linear & quadratic
- Real or complex roots
- Shows the discriminant
- Instant result
The quadratic formula
The quadratic formula solves any equation of the form ax² + bx + c = 0. The discriminant (b² − 4ac) reveals the nature of the roots before you compute them: positive gives two real roots, zero gives one repeated root, and negative gives a pair of complex conjugate roots. When a is zero, the equation is linear and has a single solution.