Solve 9/u=u/4quad

$$\frac { 9 } { u } = \frac { u } { 4 } \quad$$

Solve for u

$$u=6$$

$$u=-6$$

Steps by Finding Square Root

Variable u cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4u, the least common multiple of u,4.

$$4\times 9=uu$$

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

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

Multiply 4 and 9 to get 36.

$$36=u^{2}$$

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

$$u^{2}=36$$

Take the square root of both sides of the equation.

$$u=6 u=-6$$

Steps Using the Quadratic Formula

Variable u cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4u, the least common multiple of u,4.

$$4\times 9=uu$$

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

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

Multiply 4 and 9 to get 36.

$$36=u^{2}$$

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

$$u^{2}=36$$

Subtract 36 from both sides.

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

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}.

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

Square 0.

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

Multiply -4 times -36.

$$u=\frac{0±\sqrt{144}}{2}$$

Take the square root of 144.

$$u=\frac{0±12}{2}$$

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

$$u=6$$

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

$$u=-6$$

The equation is now solved.

$$u=6 u=-6$$