Solve the following equation using quadratic formula:

3x² - x - 7 = 0

Given,

⇒ 3x² - x - 7 = 0

Comparing equation 3x² - x - 7 = 0 with ax² + bx + c = 0, we get :

a = 3, b = -1 and c = -7.

By formula,

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

Substituting values we get :

$\Rightarrow x = \dfrac{-(-1) \pm \sqrt{(-1)^2 - 4 \times (3) \times (-7)}}{2 \times (3)} \\[1em] = \dfrac{1 \pm \sqrt{1 + 84}}{6} \\[1em] = \dfrac{1 \pm \sqrt{85}}{6} \\[1em] = \dfrac{1 + \sqrt{85}}{6} \text{ or } \dfrac{1 - \sqrt{85}}{6} \\[1em] = \dfrac{1 + 9.2195}{6} \text{ or } \dfrac{1 - 9.2195}{6} \\[1em] = \dfrac{10.2195}{6} \text{ or } \dfrac{-8.2195}{6} \\[1em] = 1.703 \approx 1.70 \text{ or } -1.369 \approx -1.37.$

Hence, x = {1.70, -1.37}.