Solve y*sqrt{3x}=7

$$y \times \sqrt { 3 x } = 7$$

Solve for y (complex solution)

$$y=\frac{7\sqrt{3}x^{-\frac{1}{2}}}{3}$$

$$x\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\sqrt{3x}y=7$$

Divide both sides by \sqrt{3x}.

$$\frac{\sqrt{3x}y}{\sqrt{3x}}=\frac{7}{\sqrt{3x}}$$

Dividing by \sqrt{3x} undoes the multiplication by \sqrt{3x}.

$$y=\frac{7}{\sqrt{3x}}$$

Divide 7 by \sqrt{3x}.

$$y=7\times \left(3x\right)^{-\frac{1}{2}}$$

Solve for x

$$x=\frac{49}{3y^{2}}$$

$$y>0$$

Steps for Solving Radical Equations

Divide both sides by y.

$$\frac{y\sqrt{3x}}{y}=\frac{7}{y}$$

Dividing by y undoes the multiplication by y.

$$\sqrt{3x}=\frac{7}{y}$$

Square both sides of the equation.

$$3x=\frac{49}{y^{2}}$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{49}{3y^{2}}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{49}{3y^{2}}$$

Solve for y

$$y=\frac{7\sqrt{\frac{3}{x}}}{3}$$

$$x>0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\sqrt{3x}y=7$$

Divide both sides by \sqrt{3x}.

$$\frac{\sqrt{3x}y}{\sqrt{3x}}=\frac{7}{\sqrt{3x}}$$

Dividing by \sqrt{3x} undoes the multiplication by \sqrt{3x}.

$$y=\frac{7}{\sqrt{3x}}$$

Solve for x (complex solution)

$$x=\frac{49}{3y^{2}}$$

$$arg(\sqrt{\frac{1}{y^{2}}}y)<\pi \text{ and }y\neq 0$$