$\begin{array}{l}
10 x-\frac{1}{x}=3 \\
\Rightarrow 10 x^{2}-1=3 x
\end{array}$
[Multiplying both sides by $x]$
$\begin{array}{l}
\Rightarrow 10 x^{2}-3 x-1=0 \\
\Rightarrow 10 x^{2}-(5 x-2 x)-1=0 \\
\Rightarrow 10 x^{2}-5 x+2 x-1=0 \\
\Rightarrow 5 x(2 x-1)+1(2 x-1)=0 \\
\Rightarrow(2 x-1)(5 x+1)=0 \\
\Rightarrow 2 x-1=0 \text { of } 5 x+1=0 \\
\Rightarrow x=\frac{1}{2} \text { or } x=\frac{-1}{5}
\end{array}$

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