Solve y^3=2ax

$$y ^ { 3 } = 2 a x$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{y^{3}}{2x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$2ax=y^{3}$$

The equation is in standard form.

$$2xa=y^{3}$$

Divide both sides by 2x.

$$\frac{2xa}{2x}=\frac{y^{3}}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$a=\frac{y^{3}}{2x}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{y^{3}}{2a}\text{, }&a\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$2ax=y^{3}$$

Divide both sides by 2a.

$$\frac{2ax}{2a}=\frac{y^{3}}{2a}$$

Dividing by 2a undoes the multiplication by 2a.

$$x=\frac{y^{3}}{2a}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{y^{3}}{2x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$2ax=y^{3}$$

The equation is in standard form.

$$2xa=y^{3}$$

Divide both sides by 2x.

$$\frac{2xa}{2x}=\frac{y^{3}}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$a=\frac{y^{3}}{2x}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{y^{3}}{2a}\text{, }&a\neq 0\\x\in \mathrm{R}\text{, }&y=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$2ax=y^{3}$$

Divide both sides by 2a.

$$\frac{2ax}{2a}=\frac{y^{3}}{2a}$$

Dividing by 2a undoes the multiplication by 2a.

$$x=\frac{y^{3}}{2a}$$