# How do you solve 3x^2 - 8x + 2 = 0 using the quadratic formula?

May 3, 2016

Use the formula:

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

to find:

$x = \frac{4 \pm \sqrt{10}}{3}$

#### Explanation:

$3 {x}^{2} - 8 x + 2 = 0$ is of the form $a {x}^{2} + b x + c = 0$, with $a = 3$, $b = - 8$ and $c = 2$

This has roots given by the quadratic formula:

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

$= \frac{8 \pm \sqrt{{\left(- 8\right)}^{2} - \left(4 \cdot 3 \cdot 2\right)}}{2 \cdot 3}$

$= \frac{8 \pm \sqrt{64 - 24}}{6}$

$= \frac{8 \pm \sqrt{40}}{6}$

$= \frac{8 \pm \sqrt{{2}^{2} \cdot 10}}{6}$

$= \frac{8 \pm 2 \sqrt{10}}{6}$

$= \frac{4 \pm \sqrt{10}}{3}$