# How do you solve x² -3x-7=0?

Aug 20, 2015

The solutions are
color(blue)(x=(3+sqrt(37))/2

color(blue)(x=(3-sqrt(37))/2

#### Explanation:

${x}^{2} - 3 x - 7 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 1 , b = - 3 , c = - 7$

The Discriminant is given by:
$\Delta = {b}^{2} - 4 \cdot a \cdot c$
$= {\left(- 3\right)}^{2} - \left(4 \cdot 1 \cdot - 7\right)$
$= 9 + 28 = 37$

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

$x = \frac{- \left(- 3\right) \pm \sqrt{37}}{2 \cdot 1} = \frac{3 \pm \sqrt{37}}{2}$

The solutions are
color(blue)(x=(3+sqrt(37))/2

color(blue)(x=(3-sqrt(37))/2