Solve 9/x=x/15

$$\frac{ 9 }{ x } = \frac{ x }{ 15 }$$

Solve for x

$$x=3\sqrt{15}\approx 11.618950039$$

$$x=-3\sqrt{15}\approx -11.618950039$$

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 15x, the least common multiple of x,15.

$$15\times 9=xx$$

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

$$15\times 9=x^{2}$$

Multiply 15 and 9 to get 135.

$$135=x^{2}$$

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

$$x^{2}=135$$

Take the square root of both sides of the equation.

$$x=3\sqrt{15} x=-3\sqrt{15}$$

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 15x, the least common multiple of x,15.

$$15\times 9=xx$$

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

$$15\times 9=x^{2}$$

Multiply 15 and 9 to get 135.

$$135=x^{2}$$

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

$$x^{2}=135$$

Subtract 135 from both sides.

$$x^{2}-135=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -135 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-135\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-135\right)}}{2}$$

Multiply -4 times -135.

$$x=\frac{0±\sqrt{540}}{2}$$

Take the square root of 540.

$$x=\frac{0±6\sqrt{15}}{2}$$

Now solve the equation x=\frac{0±6\sqrt{15}}{2} when ± is plus.

$$x=3\sqrt{15}$$

Now solve the equation x=\frac{0±6\sqrt{15}}{2} when ± is minus.

$$x=-3\sqrt{15}$$

The equation is now solved.

$$x=3\sqrt{15} x=-3\sqrt{15}$$