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

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 5\left(-2\right)}}{2\times 5}$$

$$x=\frac{-\left(-6\right)±\sqrt{36-4\times 5\left(-2\right)}}{2\times 5}$$

$$x=\frac{-\left(-6\right)±\sqrt{36-20\left(-2\right)}}{2\times 5}$$

$$x=\frac{-\left(-6\right)±\sqrt{36+40}}{2\times 5}$$

$$x=\frac{-\left(-6\right)±\sqrt{76}}{2\times 5}$$

$$x=\frac{-\left(-6\right)±2\sqrt{19}}{2\times 5}$$

$$x=\frac{6±2\sqrt{19}}{2\times 5}$$

$$x=\frac{6±2\sqrt{19}}{10}$$

$$x=\frac{2\sqrt{19}+6}{10}$$

$$x=\frac{\sqrt{19}+3}{5}$$

$$x=\frac{6-2\sqrt{19}}{10}$$

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

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

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

$$5x^{2}-6x-2-\left(-2\right)=-\left(-2\right)$$

$$5x^{2}-6x=-\left(-2\right)$$

$$5x^{2}-6x=2$$

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

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

$$x^{2}-\frac{6}{5}x+\left(-\frac{3}{5}\right)^{2}=\frac{2}{5}+\left(-\frac{3}{5}\right)^{2}$$

$$x^{2}-\frac{6}{5}x+\frac{9}{25}=\frac{2}{5}+\frac{9}{25}$$

$$x^{2}-\frac{6}{5}x+\frac{9}{25}=\frac{19}{25}$$

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

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

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

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

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

$$r + s = \frac{6}{5} $$ $$ rs = -\frac{2}{5}$$

$$r = \frac{3}{5} - u$$ $$s = \frac{3}{5} + u$$

$$(\frac{3}{5} - u) (\frac{3}{5} + u) = -\frac{2}{5}$$

$$\frac{9}{25} - u^2 = -\frac{2}{5}$$

$$-u^2 = -\frac{2}{5}-\frac{9}{25} = -\frac{19}{25}$$

$$u^2 = \frac{19}{25}$$ $$u = \pm\sqrt{\frac{19}{25}} = \pm \frac{\sqrt{19}}{5} $$

$$r =\frac{3}{5} - \frac{\sqrt{19}}{5} = -0.272$$ $$s = \frac{3}{5} + \frac{\sqrt{19}}{5} = 1.472$$