# How do you solve the quadratic using the quadratic formula given 8n^2-4n=18?

Sep 14, 2016

$n = 1.77$
$n = - 1.27$

#### Explanation:

Given -

$8 {n}^{2} - 4 n = 18$

Rewrite the equation as

$8 {n}^{2} - 4 n - 18 = 0$

The formula is -

$n = \frac{- b \pm \sqrt{{b}^{2} - \left(4 a c\right)}}{2 a}$

$n = \frac{\left(- \left(- 4\right)\right) \sqrt{{\left(- 4\right)}^{2} - \left(4 \times 8 \times \left(- 18\right)\right)}}{2 \times 8}$

$n = \frac{4 \pm \sqrt{16 - \left(- 576\right)}}{16}$
$n = \frac{4 \pm \sqrt{592}}{16}$
$n = \frac{4 \pm 24.33}{16}$
$n = \frac{4 + 24.33}{16} = \frac{28.33}{16} = 1.77$
$n = \frac{4 - 24.33}{16} = - \frac{20.33}{16} = - 1.27$