# How do you solve x^2 -3x = -7?

Aug 11, 2015

The solutions are:
color(green)(x = ((3)+sqrt(-19))/(2

color(green)(x = ((3)-sqrt(-19))/(2

#### Explanation:

x^2−3x+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:
$\Delta = {b}^{2} - 4 \cdot a \cdot c$

$= {\left(- 3\right)}^{2} - \left(4 \cdot 1 \cdot 7\right)$

$= 9 - 28 = - 19$

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

x = (-(-3)+-sqrt(-19))/(2

The solutions are:
color(green)(x = (3+sqrt(-19))/(2

color(green)(x = (3-sqrt(-19))/(2