How do I solve a quadratic equation?

The best way to solve a quadratic function is to put brackets into the equation.

Start with an example

Find x when y=0 for the function 

y=x*2 + 5x + 6

As y=0 make the whole equation= 0:

x*2 + 5x + 6=0

Try and put this into brackets:

(x+a)(x+b)=0 (as all the values are positive, we know that there are going to be no negative signs in the brackets).

Now we just need to find values for a and b that multiply out to give us the equation we need.

Try a=6 and b=1:

This gives us the 6 at the end but when multiplied out gives us 7x- which is too much.

Now try a=2 and b=3 and multply out:

We get 0=x*2+ 2x + 3x + 6= x*2 + 5x + 6 ... which is what we want!

So we get (x+2)(x+3)=0

For it to equal 0 either:

x+2=0 so x=-2 or

x+3=0 so x=-3

so x=-2, -3

Rosiered B. GCSE Biology tutor, A Level Biology tutor, GCSE Maths tut...

10 months ago

Answered by Rosiered, a GCSE Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£18 /hr

Balraj D.

Degree: PPE (Philsophy, Politics & Economics) (Bachelors) - Warwick University

Subjects offered: Maths, Philosophy+ 4 more

.TSA. Oxford.

“Hi! I'm Bal! Currently studying Philosophy, Politics and Economics in my first year at university and really enjoying myself. I got a score of 41 in my IB Diploma, 11 points above the world average. I also gained 10A*s in my GCSEs. In ...”

£18 /hr

Erin B.

Degree: Biomedical Sciences (Bachelors) - Durham University

Subjects offered: Maths, Spanish+ 1 more


“About me: I am currently in my first year studying Biomedical Sciences at Durham University. Prior to coming to the U.K., I completed the International Baccalaureate Diploma Program at an international school in Tokyo, Japan. I come ...”

MyTutor guarantee

£18 /hr

Matthew H.

Degree: Physics (Masters) - Liverpool University

Subjects offered: Maths, Physics+ 3 more

-Personal Statements-

“About Me  I am studying physics at the University of Liverpool and am now in my second year having passed with a first in all my modules last year. I really love all things science and have a real drive to pass on what I know to other...”

About the author

Rosiered B.

Currently unavailable: for new students

Degree: Biomedical sciences (Bachelors) - Durham University

Subjects offered: Maths, Psychology+ 1 more


“About meMy name is Rosiered Brownson-smith and I study Biomedical Sciences at Durham University. I have a passion for science and maths! I pride myself on being friendly, enthusiastic and approachable- so don't hesitate to get in tou...”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

How do I find the length of a side of a triangle using the cosine rule?

How should I go about factorising x^2+5x+6?

Find the inverse of y = 2x+1/ x-1

Eleri invests £3700 for 3 years at 2% per annum compound interest. Calculate the value of her investment at the end of the 3 years. Give your answer correct to the nearest penny.

View GCSE Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss