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

Aug 11, 2016

$a = \frac{- 1 \pm \sqrt{129}}{8}$

#### Explanation:

The quadratic formula takes an equation of the form $a {x}^{2} + b x + c = 0$ and gives us the solutions $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$.

Then, to use it, first we must work our equation into the desired form.

$4 {a}^{2} - 8 = a$

$\implies 4 {a}^{2} - a - 8 = 0$

Now we have an equation of the desired form. Applying the formula:

$a = \frac{- \left(- 1\right) \pm \sqrt{{\left(- 1\right)}^{2} - 4 \left(4\right) \left(- 8\right)}}{2 \left(4\right)} = \frac{- 1 \pm \sqrt{129}}{8}$