Solve the following equation using quadratic formula:

25x² + 30x + 7 = 0

Comparing equation 25x² + 30x + 7 = 0 with ax² + bx + c = 0, we get :

a = 25, b = 30 and c = 7.

By formula,

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

Substituting values we get :

$\Rightarrow x = \dfrac{-(30) \pm \sqrt{(30)^2 - 4 \times 25 \times 7}}{2(25)} \\[1em] = \dfrac{-30 \pm \sqrt{900 - 700}}{50} \\[1em] = \dfrac{-30 \pm \sqrt{200}}{50} \\[1em] = \dfrac{-30 \pm \sqrt{2 \times 100}}{50} \\[1em] = \dfrac{-30 \pm 10\sqrt{2}}{50} \\[1em] = \dfrac{10(-3 \pm \sqrt{2})}{50} \\[1em] = \dfrac{(-3 \pm \sqrt{2})}{5} \\[1em] = \dfrac{(-3 + \sqrt{2})}{5} \text{ or } \dfrac{(-3 - \sqrt{2})}{5}.$

Hence, $x = \Big{\dfrac{-3 + \sqrt{2}}{5}, \dfrac{-3 - \sqrt{2}}{5}\Big}$.