Solve 3/n=n/27

$$\frac { 3 } { n } = \frac { n } { 27 }$$

Solve for n

$$n=9$$

$$n=-9$$

Steps by Finding Square Root

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 27n, the least common multiple of n,27.

$$27\times 3=nn$$

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

$$27\times 3=n^{2}$$

Multiply 27 and 3 to get 81.

$$81=n^{2}$$

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

$$n^{2}=81$$

Take the square root of both sides of the equation.

$$n=9 n=-9$$

Steps Using the Quadratic Formula

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 27n, the least common multiple of n,27.

$$27\times 3=nn$$

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

$$27\times 3=n^{2}$$

Multiply 27 and 3 to get 81.

$$81=n^{2}$$

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

$$n^{2}=81$$

Subtract 81 from both sides.

$$n^{2}-81=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -81 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-81\right)}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-81\right)}}{2}$$

Multiply -4 times -81.

$$n=\frac{0±\sqrt{324}}{2}$$

Take the square root of 324.

$$n=\frac{0±18}{2}$$

Now solve the equation n=\frac{0±18}{2} when ± is plus. Divide 18 by 2.

$$n=9$$

Now solve the equation n=\frac{0±18}{2} when ± is minus. Divide -18 by 2.

$$n=-9$$

The equation is now solved.

$$n=9 n=-9$$