Solve frac{sqrt{2}}{2}=frac{10sqrt{3}}{x}

$$\frac{ \sqrt{ 2 } }{ 2 } = \frac{ 10 \sqrt{ 3 } }{ x }$$

Solve for x

$$x=10\sqrt{6}\approx 24.494897428$$

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 2x, the least common multiple of 2,x.

$$x\sqrt{2}=2\times 10\sqrt{3}$$

Multiply 2 and 10 to get 20.

$$x\sqrt{2}=20\sqrt{3}$$

The equation is in standard form.

$$\sqrt{2}x=20\sqrt{3}$$

Divide both sides by \sqrt{2}.

$$\frac{\sqrt{2}x}{\sqrt{2}}=\frac{20\sqrt{3}}{\sqrt{2}}$$

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

$$x=\frac{20\sqrt{3}}{\sqrt{2}}$$

Divide 20\sqrt{3} by \sqrt{2}.

$$x=10\sqrt{6}$$