Solve (1)-5x^2y=10w

$$( 1 ) - 5 x ^ { 2 } y = 10 w$$

Solve for w

$$w=-\frac{yx^{2}}{2}+\frac{1}{10}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$10w=1-5x^{2}y$$

The equation is in standard form.

$$10w=1-5yx^{2}$$

Divide both sides by 10.

$$\frac{10w}{10}=\frac{1-5yx^{2}}{10}$$

Dividing by 10 undoes the multiplication by 10.

$$w=\frac{1-5yx^{2}}{10}$$

Divide 1-5x^{2}y by 10.

$$w=-\frac{yx^{2}}{2}+\frac{1}{10}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{iy^{-\frac{1}{2}}\sqrt{50w-5}}{5}\text{; }x=\frac{iy^{-\frac{1}{2}}\sqrt{50w-5}}{5}\text{, }&y\neq 0\\x\in \mathrm{C}\text{, }&w=\frac{1}{10}\text{ and }y=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{\frac{5\left(1-10w\right)}{y}}}{5}\text{; }x=-\frac{\sqrt{\frac{5\left(1-10w\right)}{y}}}{5}\text{, }&\left(y>0\text{ and }w\leq \frac{1}{10}\right)\text{ or }\left(w\geq \frac{1}{10}\text{ and }y<0\right)\\x\in \mathrm{R}\text{, }&w=\frac{1}{10}\text{ and }y=0\end{matrix}\right.$$