$\begin{array}{l}
5 x^{2}-6 x-2=0 \\
\Rightarrow 25 x^{2}-30 x-10=0 \\
\Rightarrow 25 x^{2}-30 x=10
\end{array}$
$\begin{array}{l}
\Rightarrow(5 x)^{2}-2 \times 5 x \times 3+3^{2}=10+3^{2} \\
\Rightarrow(5 x-3)^{2}=10+9-19 \\
\Rightarrow 5 x-3=\pm \sqrt{19} \\
\Rightarrow 5 x-3=\sqrt{19} \text { or } 5 x-3=-\sqrt{19} \\
\Rightarrow 5 x=3+\sqrt{19} \text { or } 5 x=3-\sqrt{19} \\
\Rightarrow x=\frac{3+\sqrt{19}}{5} \text { or } x=\frac{3-\sqrt{19}}{5}
\end{array}$

Hence, $\frac{3+\sqrt{19}}{5}$ and $\frac{3-\sqrt{19}}{5}$ are $\frac{3-\sqrt{19}}{5}$ are the roots of the given equation.