# How do you solve 2x^2 - 15x = 8?

Jan 31, 2017

The solutions are $S = \left\{- \frac{1}{2} , 8\right\}$

#### Explanation:

Let's rewrite the equation

$2 {x}^{2} - 15 x - 8 = 0$

And compare this to the quadratic equation

$a {x}^{2} + b x + c = 0$

We start by calculating the discriminant

$\Delta = {b}^{2} - 4 a c = {\left(- 15\right)}^{2} - 4 \left(2\right) \left(- 8\right) = 225 + 64 = 289$

The solutions are

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

${x}_{1} = \frac{15 + \sqrt{289}}{2 \cdot 2} = \frac{15 + 17}{4} = 8$

${x}_{2} = \frac{15 - 17}{2 \cdot 2} = - \frac{2}{4} = - \frac{1}{2}$