Solve the following equation using quadratic formula:

6x² - 31x = 105

⇒ 6x² - 31x - 105 = 0

Comparing equation 6x² - 31x - 105 = 0 with ax² + bx + c = 0, we get :

a = 6, b = -31 and c = -105.

By formula,

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

Substituting values we get :

$\Rightarrow x = \dfrac{-(-31) \pm \sqrt{(-31)^2 - 4 \times 6 \times(-105)}}{2\times(6)} \\[1em] = \dfrac{31 \pm \sqrt{961 + 2520}}{12} \\[1em] = \dfrac{31 \pm \sqrt{3481}}{12} \\[1em] = \dfrac{31 \pm 59}{12} \\[1em] = \dfrac{31 + 59}{12} \text{ or } \dfrac{31 - 59}{12} \\[1em] = \dfrac{90}{12} \text{ or } \dfrac{-28}{12} \\[1em] = \dfrac{15}{2} \text{ or } \dfrac{-7}{3}.$

Hence, $x = \Big{\dfrac{15}{2}, \dfrac{-7}{3}\Big}$.