# How do you solve x^2+5x-84=0 using the quadratic formula?

Aug 10, 2015

The solutions for the equation are:
 color(blue)(x=7 ,  color(blue)(x=-12

#### Explanation:

x^2+5x−84=0

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 1 , b = 5 , c = - 84$

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

$= {\left(5\right)}^{2} - \left(4 \cdot 1 \cdot \left(- 84\right)\right)$

$= 25 + 336 = 361$

The solutions are found using the formula:

$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

$x = \frac{\left(- 5\right) \pm \sqrt{361}}{2 \cdot 1} = \frac{\left(- 5 \pm 19\right)}{2}$

The solutions are:
x= ((-5+19))/2 = 14/2 , color(blue)(x=7

x= ((-5-19))/2 =-24/2, color(blue)(x=-12