Solve the following equations by using formula:

10ax² - 6x + 15ax - 9 = 0 , a ≠ 0.

The given equation is 10ax² - 6x + 15ax - 9 = 0

Comparing it with ax² + bx + c = 0
a= 10a, b = (15a - 6), c = -9

By using the formula , x = $\dfrac{-b ± \sqrt{b^2 - 4ac}}{2a}$ , we obtain

$\Rightarrow \dfrac{-(15a - 6) ± \sqrt{(15a - 6)^2 - 4 \times 10a \times -9}}{2 \times 10a} \\[1em] \Rightarrow \dfrac{(6 - 15a) ± \sqrt{225a^2 + 36 - 180a + 360a}}{20a} \\[1em] \Rightarrow \dfrac{6 - 15a ± \sqrt{225a^2 + 36 + 180a}}{20a} \\[1em] \Rightarrow \dfrac{6 - 15a ± \sqrt{(15a + 6)^2}}{20a}\\[1em] \Rightarrow \dfrac{6 - 15a + |15a + 6|}{20a} \text{ or } \dfrac{6 - 15a - |15a + 6|}{20a} \\[1em] \Rightarrow \dfrac{12}{20a} \text{ or } -\dfrac{30a}{20a} \\[1em] \dfrac{3}{5a} \text{ or } -\dfrac{3}{2}$

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