Solve 3n^2=45

$$3 n ^ { 2 } = 45$$

Solve for n

$$n=\sqrt{15}\approx 3.872983346$$

$$n=-\sqrt{15}\approx -3.872983346$$

Steps by Finding Square Root

Divide both sides by 3.

$$n^{2}=\frac{45}{3}$$

Divide 45 by 3 to get 15.

$$n^{2}=15$$

Take the square root of both sides of the equation.

$$n=\sqrt{15} n=-\sqrt{15}$$

Steps Using the Quadratic Formula

Divide both sides by 3.

$$n^{2}=\frac{45}{3}$$

Divide 45 by 3 to get 15.

$$n^{2}=15$$

Subtract 15 from both sides.

$$n^{2}-15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-15\right)}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-15\right)}}{2}$$

Multiply -4 times -15.

$$n=\frac{0±\sqrt{60}}{2}$$

Take the square root of 60.

$$n=\frac{0±2\sqrt{15}}{2}$$

Now solve the equation n=\frac{0±2\sqrt{15}}{2} when ± is plus.

$$n=\sqrt{15}$$

Now solve the equation n=\frac{0±2\sqrt{15}}{2} when ± is minus.

$$n=-\sqrt{15}$$

The equation is now solved.

$$n=\sqrt{15} n=-\sqrt{15}$$