# How do you find the solutions of -5+2x^2=-6x?

Jan 10, 2017

$\frac{3 \pm \sqrt{19}}{2}$

#### Explanation:

$- 5 + 2 {x}^{2} = - 6 x$
$\Leftrightarrow 2 {x}^{2} + 6 x - 5 = 0$
$D = {d}^{2} = {b}^{2} - 4 a c = 36 + 40 = 76$ --> $d = \pm 2 \sqrt{19}$
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = - \frac{6}{4} \pm \frac{2 \sqrt{19}}{4} = \frac{3 \pm \sqrt{19}}{2}$
$x 1 = \frac{3 + \sqrt{19}}{2}$
$x 2 = \frac{3 - \sqrt{19}}{2}$