# Using the quadratic formula

**Using the quadratic formula**

The quadratic equation of the following form can be solved using the second solution:

*ax*² + *bx* + *c* = 0

For example, when using the above formula to solve 2*x*² + 5*x* – 1 = 0, the following steps are taken:

2*x*² + 5*x* – 1 = 0 (insert into the above formula format

**Using the ***b*² – 4*ac* formula further

*b*² – 4

*ac*formula further

Fort the above formula, the *b*² – 4*ac* can be used to recognise how many solution there can be:

- If
= positive – there are two solutions.*b*² – 4*ac* - If
*b*² – 40 – there is one solution.**ac**= - If
= negative – there are no solutions.*b*² – 4*ac*

This can be graphically demonstrated using the following graphs: