Solve the following equation using quadratic formula:

9x² + 7x - 2 = 0

Comparing equation 9x² + 7x - 2 = 0 with ax² + bx + c = 0, we get :

a = 9, b = 7 and c = -2.

By formula,

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

Substituting values we get :

$\Rightarrow x = \dfrac{-(7) \pm \sqrt{(7)^2 - 4 \times 9 \times (-2)}}{2(9)} \\[1em] = \dfrac{-7 \pm \sqrt{49 + 72}}{18} \\[1em] \Rightarrow x = \dfrac{-7 \pm \sqrt{121}}{18} \\[1em] = \dfrac{-7 \pm 11}{18} \\[1em] = \dfrac{-7 + 11}{18} \text{ or } \dfrac{-7 - 11}{18}\\[1em] = \dfrac{4}{18} \text{ or } \dfrac{-18}{18}\\[1em] = \dfrac{2}{9} \text{ or } -1.$

Hence, $x = \Big{\dfrac{2}{9}, -1\Big}$.