Solve (n-2/6)^2-24/25=n^2-4

$$( n - \frac { 2 } { 6 } ) ^ { 2 } - \frac { 24 } { 25 } = n ^ { 2 } - 4$$

Solve for n

$$n = \frac{709}{150} = 4\frac{109}{150} \approx 4.726666667$$

Steps for Solving Linear Equation

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\left(n-\frac{1}{3}\right)^{2}-\frac{24}{25}=n^{2}-4$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(n-\frac{1}{3}\right)^{2}.

$$n^{2}-\frac{2}{3}n+\frac{1}{9}-\frac{24}{25}=n^{2}-4$$

Subtract \frac{24}{25} from \frac{1}{9} to get -\frac{191}{225}.

$$n^{2}-\frac{2}{3}n-\frac{191}{225}=n^{2}-4$$

Subtract n^{2} from both sides.

$$n^{2}-\frac{2}{3}n-\frac{191}{225}-n^{2}=-4$$

Combine n^{2} and -n^{2} to get 0.

$$-\frac{2}{3}n-\frac{191}{225}=-4$$

Add \frac{191}{225} to both sides.

$$-\frac{2}{3}n=-4+\frac{191}{225}$$

Add -4 and \frac{191}{225} to get -\frac{709}{225}.

$$-\frac{2}{3}n=-\frac{709}{225}$$

Multiply both sides by -\frac{3}{2}, the reciprocal of -\frac{2}{3}.

$$n=-\frac{709}{225}\left(-\frac{3}{2}\right)$$

Multiply -\frac{709}{225} and -\frac{3}{2} to get \frac{709}{150}.

$$n=\frac{709}{150}$$