# How do you solve (x+6)(x-2)=9?

Mar 14, 2016

The solutions are:
$x = 3$
$x = - 7$

#### Explanation:

(x+6)(x−2)=9

$\left(x\right) \cdot \left(x\right) + x \cdot \left(- 2\right) + \left(6\right) \cdot \left(x\right) + 6 \cdot \left(- 2\right) = 9$

${x}^{2} - 2 x + 6 x - 12 = 9$

${x}^{2} + 4 x - 12 = 9$

${x}^{2} + 4 x - 12 - 9 = 0$

${x}^{2} + 4 x - 21 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 1 , b = 4 , c = - 21$

The Discriminant is given by:

$\Delta = {b}^{2} - 4 \cdot a \cdot c$

$= {\left(4\right)}^{2} - \left(4 \cdot 1 \cdot - 21\right)$

$= 16 + 84 = 100$

The solutions are found using the formula:
$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

x =( -4 +-sqrt(100))/( 2* 1

$x = \frac{- 4 + 10}{2} = \frac{6}{2} = 3$

$x = \frac{- 4 - 10}{2} = - \frac{14}{2} = - 7$