Solve yx^2+18x+4y=0

$$y x ^ { 2 } + 18 x + 4 y = 0$$

Solve for y (complex solution)

$$y=-\frac{18x}{x^{2}+4}$$

$$x\neq -2i\text{ and }x\neq 2i$$

Steps for Solving Linear Equation

Subtract 18x from both sides. Anything subtracted from zero gives its negation.

$$yx^{2}+4y=-18x$$

Combine all terms containing y.

$$\left(x^{2}+4\right)y=-18x$$

Divide both sides by x^{2}+4.

$$\frac{\left(x^{2}+4\right)y}{x^{2}+4}=-\frac{18x}{x^{2}+4}$$

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

$$y=-\frac{18x}{x^{2}+4}$$

Solve for y

$$y=-\frac{18x}{x^{2}+4}$$

Steps for Solving Linear Equation

Subtract 18x from both sides. Anything subtracted from zero gives its negation.

$$yx^{2}+4y=-18x$$

Combine all terms containing y.

$$\left(x^{2}+4\right)y=-18x$$

Divide both sides by x^{2}+4.

$$\frac{\left(x^{2}+4\right)y}{x^{2}+4}=-\frac{18x}{x^{2}+4}$$

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

$$y=-\frac{18x}{x^{2}+4}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{81-4y^{2}}-9}{y}\text{; }x=-\frac{\sqrt{81-4y^{2}}+9}{y}\text{, }&y\neq 0\\x=0\text{, }&y=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{81-4y^{2}}-9}{y}\text{; }x=-\frac{\sqrt{81-4y^{2}}+9}{y}\text{, }&y\neq 0\text{ and }|y|\leq \frac{9}{2}\\x=0\text{, }&y=0\end{matrix}\right.$$