Solve 6/x=8/sqrt{5/4}

$$\frac { 6 } { x } = \frac { 8 } { \frac { \sqrt { 5 } } { 4 } }$$

Solve for x

$$x=\frac{3\sqrt{5}}{16}\approx 0.419262746$$

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 x.

$$6=\frac{4}{5}x\times 5^{\frac{1}{2}}\times 8$$

Express \frac{4}{5}\times 8 as a single fraction.

$$6=\frac{4\times 8}{5}x\times 5^{\frac{1}{2}}$$

Multiply 4 and 8 to get 32.

$$6=\frac{32}{5}x\times 5^{\frac{1}{2}}$$

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

$$\frac{32}{5}x\times 5^{\frac{1}{2}}=6$$

Reorder the terms.

$$\frac{32}{5}\sqrt{5}x=6$$

The equation is in standard form.

$$\frac{32\sqrt{5}}{5}x=6$$

Divide both sides by \frac{32}{5}\sqrt{5}.

$$\frac{5\times \frac{32\sqrt{5}}{5}x}{32\sqrt{5}}=\frac{5\times 6}{32\sqrt{5}}$$

Dividing by \frac{32}{5}\sqrt{5} undoes the multiplication by \frac{32}{5}\sqrt{5}.

$$x=\frac{5\times 6}{32\sqrt{5}}$$

Divide 6 by \frac{32}{5}\sqrt{5}.

$$x=\frac{3\sqrt{5}}{16}$$