Solve x^2=4x+1/y

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

Solve for y

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

$$x\neq -\frac{1}{4}\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y.

$$yx^{2}=4x+1$$

The equation is in standard form.

$$x^{2}y=4x+1$$

Divide both sides by x^{2}.

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

Dividing by x^{2} undoes the multiplication by x^{2}.

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

Variable y cannot be equal to 0.

$$y=\frac{4x+1}{x^{2}}\text{, }y\neq 0$$

Solve for x (complex solution)

$$x=\frac{\sqrt{y+4}+2}{y}$$

$$x=\frac{-\sqrt{y+4}+2}{y}\text{, }y\neq 0$$

Solve for x

$$x=\frac{\sqrt{y+4}+2}{y}$$

$$x=\frac{-\sqrt{y+4}+2}{y}\text{, }y\neq 0\text{ and }y\geq -4$$