Solve frac{sqrt{6}}{x}=frac{2sqrt{5}}{5}

$$\frac { \sqrt { 6 } } { x } = \frac { 2 \sqrt { 5 } } { 5 }$$

Solve for x

$$x = \frac{\sqrt{30}}{2} \approx 2.738612788$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5x, the least common multiple of x,5.

$$5\sqrt{6}=x\times 2\sqrt{5}$$

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

$$x\times 2\sqrt{5}=5\sqrt{6}$$

The equation is in standard form.

$$2\sqrt{5}x=5\sqrt{6}$$

Divide both sides by 2\sqrt{5}.

$$\frac{2\sqrt{5}x}{2\sqrt{5}}=\frac{5\sqrt{6}}{2\sqrt{5}}$$

Dividing by 2\sqrt{5} undoes the multiplication by 2\sqrt{5}.

$$x=\frac{5\sqrt{6}}{2\sqrt{5}}$$

Divide 5\sqrt{6} by 2\sqrt{5}.

$$x=\frac{\sqrt{30}}{2}$$