Online quadratic equation solver

This page will help you to solve quadratic equations like $ax^2 + bx + c = 0$. Type your coefficient $a$, $b$ an $c$ below, the result will be updated automaticaly.

The details of the roots calculation can be found on this page.

Online calculator

$$ ax^2 + bx + c = 0 \notag $$

[ a ]

x² +

[ b ]

x +

[ c ]

= 0

Standard form

Discriminant

$$ \Delta = b^2-4ac \notag $$

If Δ > 0 => two distinct real roots.
If Δ = 0 => one repeated real root.
If Δ < 0 => two complex roots.

Two distinct real roots

Two repeated real roots

Two distinct complex roots

$$ x_1 = \dfrac{-b - i \sqrt{-\Delta}}{2a} \notag $$ $$ x_2 = \dfrac{-b + i \sqrt{-\Delta}}{2a} \notag $$