$$x^{2}+y^{2}-3x+4y^{2}-2=0$$
$x=\frac{\sqrt{17-20y^{2}}+3}{2}$
$x=\frac{-\sqrt{17-20y^{2}}+3}{2}$
$y=-\frac{\sqrt{10+15x-5x^{2}}}{5}$
$y=\frac{\sqrt{10+15x-5x^{2}}}{5}$
$x=\frac{\sqrt{17-20y^{2}}+3}{2}$
$x=\frac{-\sqrt{17-20y^{2}}+3}{2}\text{, }|y|\leq \frac{\sqrt{85}}{10}$
$y=\frac{\sqrt{10+15x-5x^{2}}}{5}$
$y=-\frac{\sqrt{10+15x-5x^{2}}}{5}\text{, }x\geq \frac{3-\sqrt{17}}{2}\text{ and }x\leq \frac{\sqrt{17}+3}{2}$