$$4x^{2}-3x+2=0$$

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

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

$$x=\frac{-\left(-3\right)±\sqrt{9-16\times 2}}{2\times 4}$$

$$x=\frac{-\left(-3\right)±\sqrt{9-32}}{2\times 4}$$

$$x=\frac{-\left(-3\right)±\sqrt{-23}}{2\times 4}$$

$$x=\frac{-\left(-3\right)±\sqrt{23}i}{2\times 4}$$

$$x=\frac{3±\sqrt{23}i}{2\times 4}$$

$$x=\frac{3±\sqrt{23}i}{8}$$

$$x=\frac{3+\sqrt{23}i}{8}$$

$$x=\frac{-\sqrt{23}i+3}{8}$$

$$x=\frac{3+\sqrt{23}i}{8}$$ $$x=\frac{-\sqrt{23}i+3}{8}$$

$$4x^{2}-3x+2=0$$

$$4x^{2}-3x+2-2=-2$$

$$4x^{2}-3x=-2$$

$$\frac{4x^{2}-3x}{4}=-\frac{2}{4}$$

$$x^{2}-\frac{3}{4}x=-\frac{2}{4}$$

$$x^{2}-\frac{3}{4}x=-\frac{1}{2}$$

$$x^{2}-\frac{3}{4}x+\left(-\frac{3}{8}\right)^{2}=-\frac{1}{2}+\left(-\frac{3}{8}\right)^{2}$$

$$x^{2}-\frac{3}{4}x+\frac{9}{64}=-\frac{1}{2}+\frac{9}{64}$$

$$x^{2}-\frac{3}{4}x+\frac{9}{64}=-\frac{23}{64}$$

$$\left(x-\frac{3}{8}\right)^{2}=-\frac{23}{64}$$

$$\sqrt{\left(x-\frac{3}{8}\right)^{2}}=\sqrt{-\frac{23}{64}}$$

$$x-\frac{3}{8}=\frac{\sqrt{23}i}{8}$$ $$x-\frac{3}{8}=-\frac{\sqrt{23}i}{8}$$

$$x=\frac{3+\sqrt{23}i}{8}$$ $$x=\frac{-\sqrt{23}i+3}{8}$$

$$x ^ 2 -\frac{3}{4}x +\frac{1}{2} = 0$$

$$r + s = \frac{3}{4} $$ $$ rs = \frac{1}{2}$$

$$r = \frac{3}{8} - u$$ $$s = \frac{3}{8} + u$$

$$(\frac{3}{8} - u) (\frac{3}{8} + u) = \frac{1}{2}$$

$$\frac{9}{64} - u^2 = \frac{1}{2}$$

$$-u^2 = \frac{1}{2}-\frac{9}{64} = \frac{23}{64}$$

$$u^2 = -\frac{23}{64}$$ $$u = \pm\sqrt{-\frac{23}{64}} = \pm \frac{\sqrt{23}}{8}i $$

$$r =\frac{3}{8} - \frac{\sqrt{23}}{8}i = 0.375 - 0.599i$$ $$s = \frac{3}{8} + \frac{\sqrt{23}}{8}i = 0.375 + 0.599i$$