Solve n^2/5=17

$$\frac { n ^ { 2 } } { 5 } = 17$$

Solve for n

$$n=\sqrt{85}\approx 9.219544457$$

$$n=-\sqrt{85}\approx -9.219544457$$

Steps by Finding Square Root

Multiply both sides by 5.

$$n^{2}=17\times 5$$

Multiply 17 and 5 to get 85.

$$n^{2}=85$$

Take the square root of both sides of the equation.

$$n=\sqrt{85} n=-\sqrt{85}$$

Steps Using the Quadratic Formula

Multiply both sides by 5.

$$n^{2}=17\times 5$$

Multiply 17 and 5 to get 85.

$$n^{2}=85$$

Subtract 85 from both sides.

$$n^{2}-85=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -85 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-85\right)}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-85\right)}}{2}$$

Multiply -4 times -85.

$$n=\frac{0±\sqrt{340}}{2}$$

Take the square root of 340.

$$n=\frac{0±2\sqrt{85}}{2}$$

Now solve the equation n=\frac{0±2\sqrt{85}}{2} when ± is plus.

$$n=\sqrt{85}$$

Now solve the equation n=\frac{0±2\sqrt{85}}{2} when ± is minus.

$$n=-\sqrt{85}$$

The equation is now solved.

$$n=\sqrt{85} n=-\sqrt{85}$$