Can you explain the formula method for solving quadratic equations?

We can use the formula method (for solving quadratic equations) to find 'roots' or values of x that satisfy or 'work out' for a given quadratic equation of an unknown variable (say x.) The formula is:

x=-b(+or- sqrt[b2-4ac])/2a

Note that the 'plus or minus' can give us 2 possible values or 'roots' for the unknown 'x'. These may be 2 positive roots, 2 negative roots, or a negative and a positive root. These roots are the coordinates where a curve/line intersects with the x axis (we know that y=0 on the x-axis already.)

We may compare our quadratic equation to the general format (ax2+bx+c) to obtain the values for a, b, and c, which are coefficients of x (c is the coefficient of x0 which equals 1.)

Our 2 values may then be substituted back into our original equation to show that the 2 sides 'match' and thus the equation is valid. We let the quadratic equation equal zero to display that the 2 sides are balanced or 'homogeneous'.


Solve the quadratic equation 3x2+9x+3 via the formula method.

Firstly, we must compare the above quadratic equation with the general format (ax2+bx+c) to obtain values for the coefficients of x. We can see that a=3, b=9, and c=3. Our general formula:

x=-b(+or- sqrt[b2-4ac])/2a

is thus

x=-9(+or- sqrt[(9)2-4(3)(3)])/2(3)

So that by solving for x, x=-0.381 (3 d.p.) and x=-2.618 (3 d.p.). We obtained these answers by adding and subtracting the square root terms (respectively) and performing the arithmetic.

We can check that these are correct by equating the quadratic to zero and substituting in our x values:



Thus our roots are correct! The equations do not equal zero exactly as we have rounded our roots to 3 decimal places.

Daniel  M. GCSE Maths tutor, GCSE Physics tutor, GCSE Biology tutor, ...

3 months ago

Answered by Daniel , a GCSE Maths tutor with MyTutor

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


£18 /hr

Jake T.

Degree: Classics (Bachelors) - St. Andrews Unversity University

Subjects offered: Maths, Latin+ 1 more

Classical Greek

“I am a Classics student at St Andrews University. I am deeply interested in language and enjoy thoroughly explaining the 'ins and outs' of Latin and Ancient Greek. These are undeniably complex languages, so it is easy to feel overwhel...”

£22 /hr

Daniel R.

Degree: Mathematics (Bachelors) - Durham University

Subjects offered: Maths, Physics+ 1 more

Further Mathematics

“About me I’m a first year student studying Maths with European Studies at Durham. I have recently taken my A levels, achieving A* in Maths and Further Maths, so I am familiar with the course content and what the examiners are looking ...”

£18 /hr

Rhoda A.

Degree: Electrical and Electronic Engineering (Masters) - Sheffield University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“A Bit About MeI have just finished my second year at The University of Sheffield, studying Electrical and Electronic Engineering.I have always wanted to teach maths, this was because I had a great teacher (my dad). I believe that e...”

About the author

Daniel M.

Currently unavailable: for regular students

Degree: Physics (Bachelors) - Bath University

Subjects offered: Maths, Science+ 4 more

-Personal Statements-

“Hi! I'm Daniel! As a patient, understanding, and industrious tutor, I aim to nourish your child's academic curiosity in a caring, understandable and encouraging manner so that they may be the best that they can be. I'm currently readi...”

You may also like...

Other GCSE Maths questions

Simplify and solve the following equation: x^2 -8x +15=0

Factorise x² + 10x + 16

Rearranging formulae

ABC is a right angled triangle. D is the point on AB such that AD = 3DB. AC = 2DB and angle A = 90 degrees. Show that sinC = k/√20 where k is an integer. Find the value of k

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