$$5x^{2}-4x+2=0$$

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

$$x=\frac{-\left(-4\right)±\sqrt{16-4\times 5\times 2}}{2\times 5}$$

$$x=\frac{-\left(-4\right)±\sqrt{16-20\times 2}}{2\times 5}$$

$$x=\frac{-\left(-4\right)±\sqrt{16-40}}{2\times 5}$$

$$x=\frac{-\left(-4\right)±\sqrt{-24}}{2\times 5}$$

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

$$x=\frac{4±2\sqrt{6}i}{2\times 5}$$

$$x=\frac{4±2\sqrt{6}i}{10}$$

$$x=\frac{4+2\sqrt{6}i}{10}$$

$$x=\frac{2+\sqrt{6}i}{5}$$

$$x=\frac{-2\sqrt{6}i+4}{10}$$

$$x=\frac{-\sqrt{6}i+2}{5}$$

$$x=\frac{2+\sqrt{6}i}{5}$$ $$x=\frac{-\sqrt{6}i+2}{5}$$

$$5x^{2}-4x+2=0$$

$$5x^{2}-4x+2-2=-2$$

$$5x^{2}-4x=-2$$

$$\frac{5x^{2}-4x}{5}=-\frac{2}{5}$$

$$x^{2}-\frac{4}{5}x=-\frac{2}{5}$$

$$x^{2}-\frac{4}{5}x+\left(-\frac{2}{5}\right)^{2}=-\frac{2}{5}+\left(-\frac{2}{5}\right)^{2}$$

$$x^{2}-\frac{4}{5}x+\frac{4}{25}=-\frac{2}{5}+\frac{4}{25}$$

$$x^{2}-\frac{4}{5}x+\frac{4}{25}=-\frac{6}{25}$$

$$\left(x-\frac{2}{5}\right)^{2}=-\frac{6}{25}$$

$$\sqrt{\left(x-\frac{2}{5}\right)^{2}}=\sqrt{-\frac{6}{25}}$$

$$x-\frac{2}{5}=\frac{\sqrt{6}i}{5}$$ $$x-\frac{2}{5}=-\frac{\sqrt{6}i}{5}$$

$$x=\frac{2+\sqrt{6}i}{5}$$ $$x=\frac{-\sqrt{6}i+2}{5}$$

$$x ^ 2 -\frac{4}{5}x +\frac{2}{5} = 0$$

$$r + s = \frac{4}{5} $$ $$ rs = \frac{2}{5}$$

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

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

$$\frac{4}{25} - u^2 = \frac{2}{5}$$

$$-u^2 = \frac{2}{5}-\frac{4}{25} = \frac{6}{25}$$

$$u^2 = -\frac{6}{25}$$ $$u = \pm\sqrt{-\frac{6}{25}} = \pm \frac{\sqrt{6}}{5}i $$

$$r =\frac{2}{5} - \frac{\sqrt{6}}{5}i = 0.400 - 0.490i$$ $$s = \frac{2}{5} + \frac{\sqrt{6}}{5}i = 0.400 + 0.490i$$