Solve (y-1)^2=x+15y=xsqrt{6}

$$( y - 1 ) ^ { 2 } = x + 15 y = x \sqrt { 6 }$$

Evaluate (complex solution)

$$\left(y-1\right)^{2}=x+15y\text{ and }x+15y=\sqrt{6}x$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{3\sqrt{120\sqrt{6}+450}}{2}-9\sqrt{20\sqrt{6}+75}+\frac{69\sqrt{6}}{2}+57\text{, }&y=-\frac{\sqrt{120\sqrt{6}+450}}{2}+\frac{3\sqrt{6}}{2}+10\\x=\frac{3\sqrt{120\sqrt{6}+450}}{2}+9\sqrt{20\sqrt{6}+75}+\frac{69\sqrt{6}}{2}+57\text{, }&y=\frac{\sqrt{120\sqrt{6}+450}}{2}+\frac{3\sqrt{6}}{2}+10\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y=-\frac{\sqrt{-210\sqrt{1710-60\sqrt{6}}-360\sqrt{285-10\sqrt{6}}+3450\sqrt{6}+12825}}{10}+\frac{17}{2}\text{, }&x=-\frac{3\sqrt{10260-360\sqrt{6}}}{5}-\frac{21\sqrt{1710-60\sqrt{6}}}{10}+\frac{69\sqrt{6}}{2}+57\\y=\frac{\sqrt{210\sqrt{1710-60\sqrt{6}}+360\sqrt{285-10\sqrt{6}}+3450\sqrt{6}+12825}}{10}+\frac{17}{2}\text{, }&x=\frac{3\sqrt{10260-360\sqrt{6}}}{5}+\frac{21\sqrt{1710-60\sqrt{6}}}{10}+\frac{69\sqrt{6}}{2}+57\end{matrix}\right.$$