Solve the following equations by using formula:

25x² + 30x + 7 = 0

The given equation is 25x² + 30x + 7 = 0.

Comparing it with ax² + bx + c = 0, we get
a = 25 , b = 30 , c = 7

By using formula,

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

we obtain:

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

Hence roots of the given equation are $\dfrac{-3 + \sqrt{2}}{5} , \dfrac{-3 - \sqrt{2}}{5}$.