Type a quadratic equation to get the solutions with full working: the discriminant, factorising, the quadratic formula, exact surd answers, decimals, the completed square form and a graph.
It follows the same steps you would write in an exam, so you can check each line of your own working.
| Method | Use it when | Learn it |
|---|---|---|
| Factorising | The numbers are small and b² − 4ac is a square number | Factorising quadratics guide |
| Quadratic formula | It does not factorise, or the question asks for decimals or an exact surd answer | Quadratic formula guide |
| Completing the square | You need the turning point, or the question asks for the form (x + p)² + q | Completing the square guide |
The quadratic formula is printed on the GCSE Higher formula sheet but not the Foundation one. See the GCSE Maths formula sheet.
A solver is great for checking, but the skill comes from doing it yourself. The quadratic formula guide has five exam-style questions with worked answers, and GCSE and A-level daily practice include quadratics regularly.
Try five quadratic formula questions →Rearrange it to ax² + bx + c = 0. If it factorises, set each bracket equal to zero. If it does not, use the quadratic formula x = (−b ± √(b² − 4ac)) / 2a, or complete the square.
The discriminant b² − 4ac tells you how many real solutions there are: two if it is positive, one repeated solution if it is zero, and none if it is negative. If it is a square number, the quadratic factorises.
When b² − 4ac is not a square number, the exact solutions contain a surd such as √3. Exam questions often ask for this exact form, or for the answer to 2 decimal places or 3 significant figures, so the solver shows all of them.
Yes. You can enter numbers like 0.5, 3/4 or −1 1/2. The solver multiplies through to whole numbers first, which does not change the solutions.
If b² − 4ac is negative, the graph never crosses the x-axis, so there are no real solutions. That is the answer expected at GCSE. For A-level Further Maths, the solver also shows the complex solutions.
Use it to check your answers and to see the method when you are stuck. Then try a similar question on your own. Exams expect you to show this working yourself.