# How do you solve using the quadratic formula 2x^2-6=-x?

Aug 30, 2016

x =3/2 or -2

#### Explanation:

Rearrange to ${x}^{2} + x - 6 = 0$
This does factorise to $\left(2 x - 3\right) \left(x + 2\right) = 0$
Giving x =3/2 or -2

The formula for solving the quadratic $a {x}^{2} + b x + c = 0$ is

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Therefore $x = \frac{- 1 \pm \sqrt{1 - \left(4 \cdot 2 \cdot - 6\right)}}{2 \cdot 2}$

$x = \frac{- 1 \pm \sqrt{1 + 48}}{4}$

$x = \frac{- 1 + 7}{4} \mathmr{and} \frac{- 1 - 7}{4}$
$x = - \frac{6}{4} = - \frac{3}{2} \mathmr{and} x = - \frac{8}{4} = - 2$