Quadratic equation solver that shows the working

Type a quadratic in $x$, such as 2x^2 - 7x + 3. Work out the roots yourself first, then open the steps and compare line by line.

How to solve a quadratic, in the order examiners expect

1. Rearrange to $a{x}^2+bx+c=0$. Everything on one side, zero on the other.
2. Try to factorise. For $2x^2-7x+3$, you need two numbers that multiply to $ac=6$ and add to $b=-7$: $-6$ and $-1$. Then $2x^2-6x-x+3=2x(x-3)-(x-3)=(2x-1)(x-3)$, so $x=\frac{1}{2}$ or $x=3$.
3. If it does not factorise, use the formula.

The part under the square root, $b^2-4ac$, is the discriminant. Positive gives two roots, zero gives one repeated root, and negative gives no real roots. You can see all three cases on the discriminant practice page.

Practise with real exam questions

• O Level 4024 quadratic equations: factorising, the formula, completing the square and word problems.
• A Level 9709 functions: quadratics inside composite and inverse functions.