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

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

Solve for x

$$x=18\sqrt{5}+45\approx 85.249223595$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

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

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

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

Multiply \frac{1}{5} and 2 to get \frac{2}{5}.

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

Subtract x from both sides.

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

Subtract \frac{1}{5}\times 5^{\frac{1}{2}}\sqrt{5} from both sides.

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

Reorder the terms.

$$\frac{2}{5}\sqrt{5}x-x=-8-\frac{1}{5}\sqrt{5}\sqrt{5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

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

Cancel out 5 and 5.

$$\frac{2}{5}\sqrt{5}x-x=-8-1$$

Subtract 1 from -8 to get -9.

$$\frac{2}{5}\sqrt{5}x-x=-9$$

Combine all terms containing x.

$$\left(\frac{2}{5}\sqrt{5}-1\right)x=-9$$

The equation is in standard form.

$$\left(\frac{2\sqrt{5}}{5}-1\right)x=-9$$

Divide both sides by \frac{2}{5}\sqrt{5}-1.

$$\frac{\left(\frac{2\sqrt{5}}{5}-1\right)x}{\frac{2\sqrt{5}}{5}-1}=-\frac{9}{\frac{2\sqrt{5}}{5}-1}$$

Dividing by \frac{2}{5}\sqrt{5}-1 undoes the multiplication by \frac{2}{5}\sqrt{5}-1.

$$x=-\frac{9}{\frac{2\sqrt{5}}{5}-1}$$

Divide -9 by \frac{2}{5}\sqrt{5}-1.

$$x=18\sqrt{5}+45$$