Solve for x
x=-\frac{2\left(y-2\right)}{y^{2}}
y\neq 0
Solve for y (complex solution)
\left\{\begin{matrix}y=\frac{\sqrt{4x+1}-1}{x}\text{; }y=-\frac{\sqrt{4x+1}+1}{x}\text{, }&x\neq 0\\y=2\text{, }&x=0\end{matrix}\right.
Solve for y
\left\{\begin{matrix}y=\frac{\sqrt{4x+1}-1}{x}\text{; }y=-\frac{\sqrt{4x+1}+1}{x}\text{, }&x\neq 0\text{ and }x\geq -\frac{1}{4}\\y=2\text{, }&x=0\end{matrix}\right.
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xy^{2}=4-2y
Subtract 2y from both sides.
y^{2}x=4-2y
The equation is in standard form.
\frac{y^{2}x}{y^{2}}=\frac{4-2y}{y^{2}}
Divide both sides by y^{2}.
x=\frac{4-2y}{y^{2}}
Dividing by y^{2} undoes the multiplication by y^{2}.
x=\frac{2\left(2-y\right)}{y^{2}}
Divide 4-2y by y^{2}.
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