Solve ksqrt{3}x=2x

$$k \sqrt { 3 } x = 2 x$$

Solve for k (complex solution)

$$\left\{\begin{matrix}\\k=\frac{2\sqrt{3}}{3}\approx 1.154700538\text{, }&\text{unconditionally}\\k\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\sqrt{3}xk=2x$$

Divide both sides by \sqrt{3}x.

$$\frac{\sqrt{3}xk}{\sqrt{3}x}=\frac{2x}{\sqrt{3}x}$$

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

$$k=\frac{2x}{\sqrt{3}x}$$

Divide 2x by \sqrt{3}x.

$$k=\frac{2\sqrt{3}}{3}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&k=\frac{2\sqrt{3}}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 2x from both sides.

$$k\sqrt{3}x-2x=0$$

Combine all terms containing x.

$$\left(k\sqrt{3}-2\right)x=0$$

The equation is in standard form.

$$\left(\sqrt{3}k-2\right)x=0$$

Divide 0 by k\sqrt{3}-2.

$$x=0$$

Solve for k

$$\left\{\begin{matrix}\\k=\frac{2\sqrt{3}}{3}\approx 1.154700538\text{, }&\text{unconditionally}\\k\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\sqrt{3}xk=2x$$

Divide both sides by \sqrt{3}x.

$$\frac{\sqrt{3}xk}{\sqrt{3}x}=\frac{2x}{\sqrt{3}x}$$

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

$$k=\frac{2x}{\sqrt{3}x}$$

Divide 2x by \sqrt{3}x.

$$k=\frac{2\sqrt{3}}{3}$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&k=\frac{2\sqrt{3}}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 2x from both sides.

$$k\sqrt{3}x-2x=0$$

Combine all terms containing x.

$$\left(k\sqrt{3}-2\right)x=0$$

The equation is in standard form.

$$\left(\sqrt{3}k-2\right)x=0$$

Divide 0 by k\sqrt{3}-2.

$$x=0$$