Solve x/4=9/x

$$\frac{ x }{ 4 } = \frac{ 9 }{ x }$$

Solve for x

$$x=6$$

$$x=-6$$

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 4x, the least common multiple of 4,x.

$$xx=4\times 9$$

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

$$x^{2}=4\times 9$$

Multiply 4 and 9 to get 36.

$$x^{2}=36$$

Take the square root of both sides of the equation.

$$x=6 x=-6$$

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 4x, the least common multiple of 4,x.

$$xx=4\times 9$$

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

$$x^{2}=4\times 9$$

Multiply 4 and 9 to get 36.

$$x^{2}=36$$

Subtract 36 from both sides.

$$x^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-36\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-36\right)}}{2}$$

Multiply -4 times -36.

$$x=\frac{0±\sqrt{144}}{2}$$

Take the square root of 144.

$$x=\frac{0±12}{2}$$

Now solve the equation x=\frac{0±12}{2} when ± is plus. Divide 12 by 2.

$$x=6$$

Now solve the equation x=\frac{0±12}{2} when ± is minus. Divide -12 by 2.

$$x=-6$$

The equation is now solved.

$$x=6 x=-6$$