Question:
$12 a b x^{2}-\left(9 a^{2}-8 b^{2}\right) x-6 a b=0$
Solution:
Given :
$12 a b x^{2}-\left(9 a^{2}-8 b^{2}\right) x-6 a b=0$
$\Rightarrow 12 a b x^{2}-9 a^{2} x+8 b^{2} x-6 a b=0$
$\Rightarrow 3 a x(4 b x-3 a)+2 b(4 b x-3 a)=0$
$\Rightarrow(3 a x+2 b)(4 b x-3 a)=0$
$\Rightarrow 3 a x+2 b=0$ or $4 b x-3 a=0$
$\Rightarrow x=\frac{-2 b}{3 a}$ or $x=\frac{3 a}{4 b}$
Hence, the roots of the equation are $\frac{-2 b}{3 a}$ and $\frac{3 a}{4 b}$.
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