Solve 9/x=x/5

$$\frac { 9 } { x } = \frac { x } { 5 }$$

Solve for x

$$x=3\sqrt{5}\approx 6.708203932$$

$$x=-3\sqrt{5}\approx -6.708203932$$

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 5x, the least common multiple of x,5.

$$5\times 9=xx$$

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

$$5\times 9=x^{2}$$

Multiply 5 and 9 to get 45.

$$45=x^{2}$$

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

$$x^{2}=45$$

Take the square root of both sides of the equation.

$$x=3\sqrt{5} x=-3\sqrt{5}$$

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 5x, the least common multiple of x,5.

$$5\times 9=xx$$

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

$$5\times 9=x^{2}$$

Multiply 5 and 9 to get 45.

$$45=x^{2}$$

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

$$x^{2}=45$$

Subtract 45 from both sides.

$$x^{2}-45=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -45 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-45\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-45\right)}}{2}$$

Multiply -4 times -45.

$$x=\frac{0±\sqrt{180}}{2}$$

Take the square root of 180.

$$x=\frac{0±6\sqrt{5}}{2}$$

Now solve the equation x=\frac{0±6\sqrt{5}}{2} when ± is plus.

$$x=3\sqrt{5}$$

Now solve the equation x=\frac{0±6\sqrt{5}}{2} when ± is minus.

$$x=-3\sqrt{5}$$

The equation is now solved.

$$x=3\sqrt{5} x=-3\sqrt{5}$$