Solve frac{x*sqrt{x}}{7y}=1x^2

$$\frac{ x \times \sqrt{ x } }{ 7y } =1 { x }^{ 2 }$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=\frac{x^{-\frac{1}{2}}}{7}\text{, }&x\neq 0\\y\neq 0\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 7y.

$$x\sqrt{x}=1x^{2}\times 7y$$

Multiply 1 and 7 to get 7.

$$x\sqrt{x}=7x^{2}y$$

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

$$7x^{2}y=x\sqrt{x}$$

The equation is in standard form.

$$7x^{2}y=\sqrt{x}x$$

Divide both sides by 7x^{2}.

$$\frac{7x^{2}y}{7x^{2}}=\frac{x^{\frac{3}{2}}}{7x^{2}}$$

Dividing by 7x^{2} undoes the multiplication by 7x^{2}.

$$y=\frac{x^{\frac{3}{2}}}{7x^{2}}$$

Divide x^{\frac{3}{2}} by 7x^{2}.

$$y=\frac{x^{-\frac{1}{2}}}{7}$$

Variable y cannot be equal to 0.

$$y=\frac{x^{-\frac{1}{2}}}{7}\text{, }y\neq 0$$

Solve for y

$$\left\{\begin{matrix}y=\frac{1}{7\sqrt{x}}\text{, }&x>0\\y\neq 0\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 7y.

$$x\sqrt{x}=1x^{2}\times 7y$$

Multiply 1 and 7 to get 7.

$$x\sqrt{x}=7x^{2}y$$

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

$$7x^{2}y=x\sqrt{x}$$

The equation is in standard form.

$$7x^{2}y=\sqrt{x}x$$

Divide both sides by 7x^{2}.

$$\frac{7x^{2}y}{7x^{2}}=\frac{x^{\frac{3}{2}}}{7x^{2}}$$

Dividing by 7x^{2} undoes the multiplication by 7x^{2}.

$$y=\frac{x^{\frac{3}{2}}}{7x^{2}}$$

Divide x^{\frac{3}{2}} by 7x^{2}.

$$y=\frac{1}{7\sqrt{x}}$$

Variable y cannot be equal to 0.

$$y=\frac{1}{7\sqrt{x}}\text{, }y\neq 0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{1}{49y^{2}}\text{, }&arg(\frac{1}{y})<\pi \text{ and }y\neq 0\\x=0\text{, }&y\neq 0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{1}{49y^{2}}\text{, }&y>0\\x=0\text{, }&y\neq 0\end{matrix}\right.$$