In this guide we’ll show you everything you need to know about the quadratic formula for GCSE maths. The quadratic formula provides a way of solving quadratic equations. We’ve previously seen how to solve quadratic equations by factorising, but this method won’t always work for every equation. For any quadratic equations where factorising won’t work, the quadratic formula will do the job. 

For any quadratic equation in this format: 

Quadratic Equation

The quadratic formula looks like this: 

The Quadratic Formula

To solve a quadratic equation using the quadratic formula, simply put the numbers from the equation into the correct place (marked a, b or c) in the formula. Simplify for a few steps and then use your calculator to get the two possible answers for x. Remember to solve once using a ‘+’ and once using a ‘–‘ after the ‘-b’ to get your two possible answers. 

Take a look at the two examples below. 

Example 1


Example quadratic equation

Start by setting out the formula, then input the numbers, simplify and solve for two possible answers. This particular equation could be factorised, but let’s practice using the formula to solve this one. For this equation a = 1, b = 6 and c = 5

Worked example 1

Example 2


Worked example 2

Use this same process for each of the quadratic equations you need to solve. You will need to learn this formula, as it won’t be given to you in the exam. Keep using it and practicing some questions and you’ll soon commit it to memory. Try writing the formula out from memory at the start of each practice question you do. Then check to see if you’re right. In no time at all you’ll find that you remember it perfectly every time.

Another good place for some extra revision on this topic is BBC bitesize. Remember you can also always contact us directly to book a trial lesson with one of our expert maths tutors.

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