Solve 4x^2=1/y+4

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

Solve for y

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

$$x\neq 0$$

Steps for Solving Linear Equation

Variable y cannot be equal to -4 since division by zero is not defined. Multiply both sides of the equation by y+4.

$$4x^{2}\left(y+4\right)=1$$

Use the distributive property to multiply 4x^{2} by y+4.

$$4x^{2}y+16x^{2}=1$$

Subtract 16x^{2} from both sides.

$$4x^{2}y=1-16x^{2}$$

Divide both sides by 4x^{2}.

$$\frac{4x^{2}y}{4x^{2}}=\frac{1-16x^{2}}{4x^{2}}$$

Dividing by 4x^{2} undoes the multiplication by 4x^{2}.

$$y=\frac{1-16x^{2}}{4x^{2}}$$

Divide -16x^{2}+1 by 4x^{2}.

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

Variable y cannot be equal to -4.

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

Solve for x (complex solution)

$$x=-\frac{\left(y+4\right)^{-\frac{1}{2}}}{2}$$

$$x=\frac{\left(y+4\right)^{-\frac{1}{2}}}{2}\text{, }y\neq -4$$

Solve for x

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

$$x=-\frac{1}{2\sqrt{y+4}}\text{, }y>-4$$