Resolver x^2-3x=-y^2+y

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

Resolva para x (complex solution)

$$x=\frac{\sqrt{9+4y-4y^{2}}+3}{2}$$

$$x=\frac{-\sqrt{9+4y-4y^{2}}+3}{2}$$

Resolva para y (complex solution)

$$y=\frac{\sqrt{1+12x-4x^{2}}+1}{2}$$

$$y=\frac{-\sqrt{1+12x-4x^{2}}+1}{2}$$

Resolva para x

$$x=\frac{\sqrt{9+4y-4y^{2}}+3}{2}$$

$$x=\frac{-\sqrt{9+4y-4y^{2}}+3}{2}\text{, }y\geq \frac{1-\sqrt{10}}{2}\text{ and }y\leq \frac{\sqrt{10}+1}{2}$$

Resolva para y

$$y=\frac{\sqrt{1+12x-4x^{2}}+1}{2}$$

$$y=\frac{-\sqrt{1+12x-4x^{2}}+1}{2}\text{, }x\geq \frac{3-\sqrt{10}}{2}\text{ and }x\leq \frac{\sqrt{10}+3}{2}$$