Prove that

Given:

$10 x-\frac{1}{x}=3$

$\Rightarrow 10 x^{2}-1=3 x \quad[$ Multiplying both sides by $x]$

$\Rightarrow 10 x^{2}-3 x-1=0$

$\Rightarrow 10 x^{2}-(5 x-2 x)-1=0$

$\Rightarrow 10 x^{2}-5 x+2 x-1=0$

$\Rightarrow 5 x(2 x-1)+1(2 x-1)=0$

$\Rightarrow(2 x-1)(5 x+1)=0$

$\Rightarrow 2 x-1=0$ or $5 x+1=0$

$\Rightarrow x=\frac{1}{2}$ or $x=\frac{-1}{5}$

Hence, the roots of the equation are $\frac{1}{2}$ and $\frac{-1}{5}$.