Find the roots of the equation $5x^2-6x-2=0$ by the method of completing the square.

Given equation: $5x^2-6x-2=0$

Using the completing square method, we first divide the equation by 5 then try to make the left side of the equation a perfect square. 

$5x^2-6x-2=0$

$\Rightarrow x^2-\frac{6}{5}x-\frac{2}{5}=0$ 

$\Rightarrow x^2-\frac{6}{5}x=\frac{2}{5}$ 

$\Rightarrow x^2-2\times \left(x\right)\times \left(\frac{3}{5}\right)+{\left(\frac{3}{5}\right)}^{\mathbf{2}}=\frac{2}{5}+{\left(\frac{3}{5}\right)}^{\mathbf{2}}$

$\Rightarrow {\left(x-\frac{3}{5}\right)}^2=\frac{2}{5}+\frac{9}{25}$

$\Rightarrow {\left(x-\frac{3}{5}\right)}^2=\frac{10}{25}+\frac{9}{25}$

$\Rightarrow {\left(x-\frac{3}{5}\right)}^2=\frac{19}{25}$

$\Rightarrow x-\frac{3}{5}=\pm \frac{\sqrt{19}}{5}$ 

$\Rightarrow x=\frac{3\pm \sqrt{19}}{5}$ 

Hence, the value of the roots is $\frac{\mathbf{3}\mathbf{\pm }\sqrt{\mathbf{19}}}{\mathbf{5}}$.