Solve frac{2sqrt{7}-x}{sqrt{5}}=x/4

$$\frac { 2 \sqrt { 7 } - x } { \sqrt { 5 } } = \frac { x } { 4 }$$

Solve for x

$$x = \frac{32 \sqrt{7} - 8 \sqrt{35}}{11} \approx 3.394127608$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4.

$$\frac{4}{5}\times 5^{\frac{1}{2}}\left(2\sqrt{7}-x\right)=x$$

Use the distributive property to multiply \frac{4}{5}\times 5^{\frac{1}{2}} by 2\sqrt{7}-x.

$$\frac{4}{5}\times 5^{\frac{1}{2}}\times 2\sqrt{7}+\frac{4}{5}\times 5^{\frac{1}{2}}\left(-1\right)x=x$$

Express \frac{4}{5}\times 2 as a single fraction.

$$\frac{4\times 2}{5}\times 5^{\frac{1}{2}}\sqrt{7}+\frac{4}{5}\times 5^{\frac{1}{2}}\left(-1\right)x=x$$

Multiply 4 and 2 to get 8.

$$\frac{8}{5}\times 5^{\frac{1}{2}}\sqrt{7}+\frac{4}{5}\times 5^{\frac{1}{2}}\left(-1\right)x=x$$

Multiply \frac{4}{5} and -1 to get -\frac{4}{5}.

$$\frac{8}{5}\times 5^{\frac{1}{2}}\sqrt{7}-\frac{4}{5}\times 5^{\frac{1}{2}}x=x$$

Subtract x from both sides.

$$\frac{8}{5}\times 5^{\frac{1}{2}}\sqrt{7}-\frac{4}{5}\times 5^{\frac{1}{2}}x-x=0$$

Subtract \frac{8}{5}\times 5^{\frac{1}{2}}\sqrt{7} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{4}{5}\times 5^{\frac{1}{2}}x-x=-\frac{8}{5}\times 5^{\frac{1}{2}}\sqrt{7}$$

Reorder the terms.

$$-\frac{4}{5}\sqrt{5}x-x=-\frac{8}{5}\sqrt{5}\sqrt{7}$$

To multiply \sqrt{5} and \sqrt{7}, multiply the numbers under the square root.

$$-\frac{4}{5}\sqrt{5}x-x=-\frac{8}{5}\sqrt{35}$$

Combine all terms containing x.

$$\left(-\frac{4}{5}\sqrt{5}-1\right)x=-\frac{8}{5}\sqrt{35}$$

The equation is in standard form.

$$\left(-\frac{4\sqrt{5}}{5}-1\right)x=-\frac{8\sqrt{35}}{5}$$

Divide both sides by -\frac{4}{5}\sqrt{5}-1.

$$\frac{\left(-\frac{4\sqrt{5}}{5}-1\right)x}{-\frac{4\sqrt{5}}{5}-1}=-\frac{\frac{8\sqrt{35}}{5}}{-\frac{4\sqrt{5}}{5}-1}$$

Dividing by -\frac{4}{5}\sqrt{5}-1 undoes the multiplication by -\frac{4}{5}\sqrt{5}-1.

$$x=-\frac{\frac{8\sqrt{35}}{5}}{-\frac{4\sqrt{5}}{5}-1}$$

Divide -\frac{8\sqrt{35}}{5} by -\frac{4}{5}\sqrt{5}-1.

$$x=-\frac{8\sqrt{7}\left(\sqrt{5}-4\right)}{11}$$