Equation Solver

Solve linear and quadratic equations and get real or complex roots.

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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

  1. Type your values into the fields above — pick your currency or units where the calculator offers them.
  2. Results update automatically as you type; there's no submit button and nothing is sent to a server.
  3. 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.

Frequently Asked Questions

What if a is zero?

Then the equation is linear (bx + c = 0) and the solver returns the single solution x = −c ÷ b.

What are complex roots?

When the discriminant is negative, the roots involve the imaginary unit i. The solver expresses them as a real part plus or minus an imaginary part.

Is this calculator free and private?

Yes. It's completely free with no signup, and every calculation runs locally in your browser, so your numbers never leave your device.