Question:
$4 x^{2}-9 x=100$
Solution:
Given:
$4 x^{2}-9 x=100$
$\Rightarrow 4 x^{2}-9 x-100=0$
$\Rightarrow 4 x^{2}-(25 x-16 x)-100=0$
$\Rightarrow 4 x^{2}-25 x+16 x-100=0$
$\Rightarrow x(4 x-25)+4(4 x-25)=0$
$\Rightarrow(4 x-25)(x+4)=0$
$\Rightarrow 4 x-25=0$ or $x+4=0$
$\Rightarrow x=\frac{25}{4}$ or $x=-4$
Hence, the roots of the equation are $\frac{25}{4}$ and $-4$.
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