Solve 5+x/sqrt{5}=x/5-3/2sqrt{5}

$$5 + \frac { x } { \sqrt { 5 } } = \frac { x } { 5 } - \frac { 3 } { 2 \sqrt { 5 } }$$

Solve for x

$$x=\frac{-53\sqrt{5}-65}{8}\approx -22.938950351$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$25+5^{\frac{1}{2}}x=x-\frac{1}{2}\times 5^{\frac{1}{2}}\times 3$$

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$25+5^{\frac{1}{2}}x=x-\frac{3}{2}\times 5^{\frac{1}{2}}$$

Subtract x from both sides.

$$25+5^{\frac{1}{2}}x-x=-\frac{3}{2}\times 5^{\frac{1}{2}}$$

Subtract 25 from both sides.

$$5^{\frac{1}{2}}x-x=-\frac{3}{2}\times 5^{\frac{1}{2}}-25$$

Reorder the terms.

$$\sqrt{5}x-x=-\frac{3}{2}\sqrt{5}-25$$

Combine all terms containing x.

$$\left(\sqrt{5}-1\right)x=-\frac{3}{2}\sqrt{5}-25$$

The equation is in standard form.

$$\left(\sqrt{5}-1\right)x=-\frac{3\sqrt{5}}{2}-25$$

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

$$\frac{\left(\sqrt{5}-1\right)x}{\sqrt{5}-1}=\frac{-\frac{3\sqrt{5}}{2}-25}{\sqrt{5}-1}$$

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

$$x=\frac{-\frac{3\sqrt{5}}{2}-25}{\sqrt{5}-1}$$

Divide -\frac{3\sqrt{5}}{2}-25 by \sqrt{5}-1.

$$x=\frac{-53\sqrt{5}-65}{8}$$