Solve frac{2sqrt{5}-2}{x}=4/25+2

$$\frac { 2 \sqrt { 5 } - 2 } { x } = \frac { 4 } { 25 + 2 }$$

Solve for x

$$x = \frac{27 {(\sqrt{5} - 1)}}{2} \approx 16.686917696$$

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.

$$2\sqrt{5}-2=\frac{1}{27}x\times 4$$

Multiply \frac{1}{27} and 4 to get \frac{4}{27}.

$$2\sqrt{5}-2=\frac{4}{27}x$$

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

$$\frac{4}{27}x=2\sqrt{5}-2$$

Divide both sides of the equation by \frac{4}{27}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{4}{27}x}{\frac{4}{27}}=\frac{2\sqrt{5}-2}{\frac{4}{27}}$$

Dividing by \frac{4}{27} undoes the multiplication by \frac{4}{27}.

$$x=\frac{2\sqrt{5}-2}{\frac{4}{27}}$$

Divide 2\sqrt{5}-2 by \frac{4}{27} by multiplying 2\sqrt{5}-2 by the reciprocal of \frac{4}{27}.

$$x=\frac{27\sqrt{5}-27}{2}$$