# How do you solve x(x-7) = 12?

May 27, 2015

Given $x \left(x - 7\right) = 12$
we can convert the given form into a standard parabolic quadratic and solve using one of several techniques to obtain the solution(s).

$x \left(x - 7\right) = 12$

${x}^{2} - 7 x - 12 = 0$

For a quadratic in the form
$a {x}^{2} + b x + c = 0$
we can use the quadratic formula for roots
$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

In this case
$x = \frac{7 \pm \sqrt{49 + 48}}{2}$

$x = \frac{7 \pm \sqrt{97}}{2}$