Solve y^2+xy+4x=7

$$y ^ { 2 } + x y + 4 x = 7$$

Solve for x

$$x=-\frac{y^{2}-7}{y+4}$$

$$y\neq -4$$

Steps for Solving Linear Equation

Subtract y^{2} from both sides.

$$xy+4x=7-y^{2}$$

Combine all terms containing x.

$$\left(y+4\right)x=7-y^{2}$$

Divide both sides by y+4.

$$\frac{\left(y+4\right)x}{y+4}=\frac{7-y^{2}}{y+4}$$

Dividing by y+4 undoes the multiplication by y+4.

$$x=\frac{7-y^{2}}{y+4}$$

Solve for y (complex solution)

$$y=\frac{\sqrt{\left(x-14\right)\left(x-2\right)}-x}{2}$$

$$y=\frac{-\sqrt{\left(x-14\right)\left(x-2\right)}-x}{2}$$

Solve for y

$$y=\frac{\sqrt{\left(x-14\right)\left(x-2\right)}-x}{2}$$

$$y=\frac{-\sqrt{\left(x-14\right)\left(x-2\right)}-x}{2}\text{, }x\leq 2\text{ or }x\geq 14$$