# How do you solve 6x^2 + 8x = 14?

Sep 9, 2015

This equation has 2 real solutions: ${x}_{1} = - 2 \frac{1}{3}$ and ${x}_{2} = 1$

#### Explanation:

Before further calculations you have to move $14$ to the left:

$6 {x}^{2} + 8 x - 14 = 0$

Now you can divide both sides by $2$:

$3 {x}^{2} + 4 x - 7 = 0$

Now you can calculate the discriminant:

$\Delta = {4}^{2} - 4 \cdot 3 \cdot \left(- 7\right) = 16 + 84 = 100$
$\sqrt{\Delta} = 10$

${x}_{1} = \frac{- b - \sqrt{\Delta}}{2 \cdot a} = \frac{- 4 - 10}{2 \cdot 3} = - \frac{14}{6} = - 2 \frac{1}{3}$

${x}_{2} = \frac{- b + \sqrt{\Delta}}{2 \cdot a} = \frac{- 4 + 10}{2 \cdot 3} = \frac{6}{6} = 1$