# How do you solve 5x^2 - 10x - 12 = 0 ?

Aug 8, 2015

Use the quadratic formula to find:

$x = 1 \pm \frac{\sqrt{85}}{5}$

#### Explanation:

$5 {x}^{2} - 10 x - 12$ is of the form $a {x}^{2} + b x + c$ with $a = 5$, $b = - 10$ and $c = - 12$

This has discriminant $\Delta$ given by the formula:

$\Delta = {b}^{2} - 4 a c = {\left(- 10\right)}^{2} - \left(4 \times 5 \times - 12\right)$

$= 100 + 240 = 340 = {2}^{2} \cdot 85$

This is positive, but not a perfect square, so the quadratic equation has a pair of irrational roots, given by the quadratic formula:

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

$= \frac{10 \pm \sqrt{340}}{10}$

$= \frac{10 \pm 2 \sqrt{85}}{10}$

$= 1 \pm \frac{\sqrt{85}}{5}$