Solve the following equations by using formula:

x² + (4 - 3a)x - 12a = 0

The given equation is x² + (4 - 3a)x - 12a = 0

Comparing it with ax² + bx + c = 0
a= 1, b = (4 - 3a), c = -12a

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

$\Rightarrow \dfrac{-(4 - 3a) ± \sqrt{(4 - 3a)^2 - 4 \times 1 \times -12a}}{2 \times 1} \\[1em] \Rightarrow \dfrac{(3a - 4) ± \sqrt{16 + 9a^2 - 24a + 48a}}{2} \\[1em] \Rightarrow \dfrac{3a - 4 ± \sqrt{16 + 9a^2 + 24a}}{2} \\[1em] \Rightarrow \dfrac{3a - 4 ± \sqrt{(4 + 3a)^2}}{2}\\[1em] \Rightarrow \dfrac{3a - 4 + |4 + 3a|}{2} \text{ or } \dfrac{3a - 4 - |4 + 3a|}{2} \\[1em] \Rightarrow \dfrac{6a}{2} \text{ or } -\dfrac{8}{2} \\[1em] 3a \text{ or } -4$

Hence, roots of the given equation are 3a, -4.