$$5w^{2}-3w+6=0$$

$$w=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 5\times 6}}{2\times 5}$$

$$w=\frac{-\left(-3\right)±\sqrt{9-4\times 5\times 6}}{2\times 5}$$

$$w=\frac{-\left(-3\right)±\sqrt{9-20\times 6}}{2\times 5}$$

$$w=\frac{-\left(-3\right)±\sqrt{9-120}}{2\times 5}$$

$$w=\frac{-\left(-3\right)±\sqrt{-111}}{2\times 5}$$

$$w=\frac{-\left(-3\right)±\sqrt{111}i}{2\times 5}$$

$$w=\frac{3±\sqrt{111}i}{2\times 5}$$

$$w=\frac{3±\sqrt{111}i}{10}$$

$$w=\frac{3+\sqrt{111}i}{10}$$

$$w=\frac{-\sqrt{111}i+3}{10}$$

$$w=\frac{3+\sqrt{111}i}{10}$$ $$w=\frac{-\sqrt{111}i+3}{10}$$

$$5w^{2}-3w+6=0$$

$$5w^{2}-3w+6-6=-6$$

$$5w^{2}-3w=-6$$

$$\frac{5w^{2}-3w}{5}=-\frac{6}{5}$$

$$w^{2}-\frac{3}{5}w=-\frac{6}{5}$$

$$w^{2}-\frac{3}{5}w+\left(-\frac{3}{10}\right)^{2}=-\frac{6}{5}+\left(-\frac{3}{10}\right)^{2}$$

$$w^{2}-\frac{3}{5}w+\frac{9}{100}=-\frac{6}{5}+\frac{9}{100}$$

$$w^{2}-\frac{3}{5}w+\frac{9}{100}=-\frac{111}{100}$$

$$\left(w-\frac{3}{10}\right)^{2}=-\frac{111}{100}$$

$$\sqrt{\left(w-\frac{3}{10}\right)^{2}}=\sqrt{-\frac{111}{100}}$$

$$w-\frac{3}{10}=\frac{\sqrt{111}i}{10}$$ $$w-\frac{3}{10}=-\frac{\sqrt{111}i}{10}$$

$$w=\frac{3+\sqrt{111}i}{10}$$ $$w=\frac{-\sqrt{111}i+3}{10}$$

$$x ^ 2 -\frac{3}{5}x +\frac{6}{5} = 0$$

$$r + s = \frac{3}{5} $$ $$ rs = \frac{6}{5}$$

$$r = \frac{3}{10} - u$$ $$s = \frac{3}{10} + u$$

$$(\frac{3}{10} - u) (\frac{3}{10} + u) = \frac{6}{5}$$

$$\frac{9}{100} - u^2 = \frac{6}{5}$$

$$-u^2 = \frac{6}{5}-\frac{9}{100} = \frac{111}{100}$$

$$u^2 = -\frac{111}{100}$$ $$u = \pm\sqrt{-\frac{111}{100}} = \pm \frac{\sqrt{111}}{10}i $$

$$r =\frac{3}{10} - \frac{\sqrt{111}}{10}i = 0.300 - 1.054i$$ $$s = \frac{3}{10} + \frac{\sqrt{111}}{10}i = 0.300 + 1.054i$$