Solve 5x=4/x

$$5 x = \frac { 4 } { x }$$

Solve for x

$$x=\frac{2\sqrt{5}}{5}\approx 0.894427191$$

$$x=-\frac{2\sqrt{5}}{5}\approx -0.894427191$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$5xx=4$$

Multiply x and x to get x^{2}.

$$5x^{2}=4$$

Divide both sides by 5.

$$x^{2}=\frac{4}{5}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$5xx=4$$

Multiply x and x to get x^{2}.

$$5x^{2}=4$$

Subtract 4 from both sides.

$$5x^{2}-4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-4\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-4\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-4\right)}}{2\times 5}$$

Multiply -20 times -4.

$$x=\frac{0±\sqrt{80}}{2\times 5}$$

Take the square root of 80.

$$x=\frac{0±4\sqrt{5}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±4\sqrt{5}}{10}$$

Now solve the equation x=\frac{0±4\sqrt{5}}{10} when ± is plus.

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

Now solve the equation x=\frac{0±4\sqrt{5}}{10} when ± is minus.

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

The equation is now solved.

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