We write, $-3 \sqrt{5} x=-2 \sqrt{5} x-\sqrt{5} x$ as $x^{2} \times 10=10 x^{2}=(-2 \sqrt{5} x) \times(-\sqrt{5} x)$

$\begin{array}{l}
\therefore x^{2}-3 \sqrt{5} x+10=0 \\
\Rightarrow x^{2}-2 \sqrt{5} x-\sqrt{5} x+10=0 \\
\Rightarrow x(x-2 \sqrt{5})-\sqrt{5}(x-2 \sqrt{5})=0 \\
\Rightarrow(x-2 \sqrt{5})(x-\sqrt{5})=0 \\
\Rightarrow x(x-2 \sqrt{5})-\sqrt{5}(x-2 \sqrt{5})=0
\end{array}$

Hence, the roots of the given equation are $\sqrt{5}$ and $2 \sqrt{5}$.