# How do you solve x^2 - 3x = 40  by quadratic formula?

Jan 13, 2016

The solutions are
color(blue)(x=8 , x=-5

#### Explanation:

${x}^{2} - 3 x - 40 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 1 , b = - 3 , c = - 40$

The Discriminant is given by:
$\Delta = {b}^{2} - 4 \cdot a \cdot c$

$= {\left(- 3\right)}^{2} - \left(4 \cdot 1 \cdot \left(- 40\right)\right)$

$= 9 + 160 = 169$

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

$x = \frac{- \left(- 3\right) \pm \sqrt{169}}{2 \cdot 1} = \frac{3 \pm 13}{2}$

x= (3 +13)/2 = 16/2 = color(blue)(8

x= (3 -13)/2 = -10/2 = color(blue)(-5