# How do you solve 27 x + 4 = 40 x ^2 using the quadratic formula?

May 12, 2017

$\frac{4}{5} \mathmr{and} \left(- \frac{1}{8}\right)$

#### Explanation:

$y = 40 {x}^{2} - 27 x - 4 = 0$
$D = {d}^{2} = {b}^{2} - 4 a c = 729 + 640 = 1369$ --> $d = \pm 37$
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = \frac{27}{80} \pm \frac{37}{80} = \frac{27 \pm 37}{80}$
$x 1 = \frac{64}{80} = \frac{4}{5}$
$x 2 = - \frac{10}{80} = - \frac{1}{8}$