Solve the following equation using quadratic formula:

3x² - 8x + 2 = 0

Comparing equation 3x² - 8x + 2 = 0 with ax² + bx + c = 0, we get :

a = 3, b = -8 and c = 2.

By formula,

x = $\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Substituting values we get :

$\Rightarrow x = \dfrac{-(-8) \pm \sqrt{(-8)^2 - 4 \times 3 \times 2}}{2\times 3} \\[1em] = \dfrac{8 \pm \sqrt{64 - 24}}{6} \\[1em] = \dfrac{8 \pm \sqrt{40}}{6} \\[1em] = \dfrac{8 \pm \sqrt{4 \times 10}}{6} \\[1em] = \dfrac{8 \pm 2\sqrt{10}}{6} \\[1em] = \dfrac{2(4 \pm \sqrt{10})}{6} \\[1em] = \dfrac{(4 \pm \sqrt{10})}{3} \\[1em] = \dfrac{4 + \sqrt{10}}{3} \text{ or} \dfrac{4 - \sqrt{10}}{3}.$

Hence, $x = \Big{\dfrac{4 + \sqrt{10}}{3}, \dfrac{4 - \sqrt{10}}{3}\Big}$.