# How do you solve x^2 – 3x – 23 = 5?

Mar 29, 2016

The solutions are:
x= color(blue)(7

x = color(blue)(-4

#### Explanation:

${x}^{2} - 3 x - 23 = 5$

${x}^{2} - 3 x - 23 - 5 = 0$

${x}^{2} - 3 x - 28 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 1 , b = - 3 , c = - 28$

The Discriminant is given by:

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

$= {\left(- 3\right)}^{2} - \left(4 \cdot 1 \cdot \left(- 28\right)\right)$

$= 9 + 112 = 121$

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

$x = \frac{- \left(- 3\right) \pm \sqrt{121}}{2 \cdot 1} = \frac{3 \pm 11}{2}$

x = (3+ 11)/2 = 14/2 = color(blue)(7

x = (3-11)/2 = -8/2 = color(blue)(-4