# How do you solve 3x² = 2x +4?

Jan 20, 2017

First, rewrite it as $3 {x}^{2} - 2 x - 4 = 0$, then use the quadratic formula and you find the roots to be $x = \frac{1 \pm \sqrt{13}}{3}$

#### Explanation:

Once you have it in the form $3 {x}^{2} - 2 x - 4 = 0$, the quadratic formula gives a reliable means of finding the roots:

$x = \frac{2 \pm \sqrt{{\left(- 2\right)}^{2} - 4 \left(3\right) \left(- 4\right)}}{2 \left(3\right)} = \frac{2 \pm \sqrt{52}}{6} = \frac{2 \pm 2 \sqrt{13}}{6}$

Now, just divide each term by 2:

$x = \frac{1 \pm \sqrt{13}}{3}$