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Quadratic Equation Calculator

Find real or complex roots and handle a linear equation when a equals zero.

Your numbers

Make it your own
Updates as you type
Two real roots
3, 2

Calculated from your inputs · rounded for display

Root 13
Root 22

Your calculation, step by step

No black boxes
  1. Solve 1x² + -5x + 6 = 0.
  2. Discriminant = b² − 4ac = 1.
  3. Compute the roots with a cancellation-resistant quadratic formula.

How to use this calculator

  1. Enter your own values in the labeled fields. Check the units and assumptions before comparing results. Only the fields needed for your selected calculation mode are shown.
  2. Your answer updates automatically. Review the calculation steps to see exactly how it was calculated.
  3. Copy, share, save, or download your result. Saved inputs stay on this device.

How the calculation works

x = [−b ± √(b² − 4ac)] / (2a)

The discriminant distinguishes two real roots, a repeated root and complex conjugate roots. For real roots the implementation uses a cancellation-resistant equivalent of the quadratic formula. If a is zero, it solves the remaining linear equation or identifies the constant equation. Extremely ill-conditioned inputs remain subject to floating-point limits.

A worked example

For x² − 5x + 6 = 0, the discriminant is 25 − 24 = 1 and the roots are 3 and 2.

Reading your result

Use the main result together with its units and supporting figures. Display values are rounded; calculations keep their underlying precision. A change in inputs or assumptions can change the answer. Compare the step-by-step working with your intended use before relying on an estimate.

Frequently asked questions

What if the discriminant is negative?

The result shows complex conjugate roots.

Can a be zero?

Yes. The calculator switches to the appropriate degenerate equation.

Sources & methodology

This calculator uses the mathematical identity and assumptions stated above. No current rates, prices, or external data are loaded. Conversion tools use international unit definitions.

Formula review: October 24, 2026. Read our methodology.