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 $-4$.