# How do you solve 2/3 x^2 + 1/4 x= 3?

Jan 25, 2016

$x = \frac{- 3 \pm 3 \sqrt{129}}{16}$

#### Explanation:

First simplify $\frac{2}{3} {x}^{2} + \frac{1}{4} x = 3$ by multiplying everything by $12$ to clear the fractions:

$8 {x}^{2} + 3 x = 36$

Re-write in standard $a {x}^{2} + b x + c = 0$ form
$8 {x}^{2} + 3 x - 36 = 0$

Apply the quadratic formula $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$ to obtain the roots.

$x = \frac{- 3 \pm \sqrt{9 - 4 \left(8\right) \left(- 36\right)}}{2 \left(8\right)}$

Simplify
$x = - \frac{3 \pm 3 \sqrt{129}}{16}$