Solve the following equation using quadratic formula:

3x² - 32x + 12 = 0

Given,

⇒ 3x² - 32x + 12 = 0

Comparing equation 3x² - 32x + 12 = 0 with ax² + bx + c = 0, we get :

a = 3, b = -32 and c = 12.

By formula,

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

Substituting values we get :

$\Rightarrow x = \dfrac{-(-32) \pm \sqrt{(-32)^2 - 4 \times 3 \times (12)}}{2 \times (3)} \\[1em] = \dfrac{32 \pm \sqrt{1024 - 144}}{6} \\[1em] = \dfrac{32 \pm \sqrt{880}}{6} \\[1em] = \dfrac{32 \pm \sqrt{4 \times 220}}{6} \\[1em] = \dfrac{32 \pm 2\sqrt{220}}{6} \\[1em] = \dfrac{32 + 2\sqrt{220}}{6} \text{ or } \dfrac{32 - 2\sqrt{220}}{6} \\[1em] = \dfrac{2(16 + \sqrt{220})}{6} \text{ or } \dfrac{2(16 - \sqrt{220})}{6} \\[1em] = \dfrac{16 + \sqrt{220}}{3} \text{ or } \dfrac{16 - \sqrt{220}}{3} \\[1em] = \dfrac{16 + 14.83}{3} \text{ or } \dfrac{16 - 14.83}{3} \\[1em] = \dfrac{30.83}{3} \text{ or } \dfrac{1.17}{3} \\[1em] = 10.28 \text{ or } 0.39$

Hence, x = {10.28, 0.39}.