# How do you factor and solve x^2 - x - 20 = 0?

Jun 12, 2016

The solutions for the equation are: color(blue)(x=-4, x = 5

#### Explanation:

${x}^{2} - x - 20 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:

$a = 1 , b = - 1 , c = - 20$

The Discriminant is given by:

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

$= {\left(- 1\right)}^{2} - \left(4 \cdot 1 \cdot \left(- 20\right)\right)$

$= 1 + 80 = 81$

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

$x = \frac{- \left(- 1\right) \pm \sqrt{81}}{2 \cdot 1} = \frac{1 \pm 9}{2}$

 x = (1+ 9 )/2 =10 /2, color(blue)( x= 5

 x = (1 - 9 )/2 = -8/2 , color(blue)(x= - 4