Solve 27n^2+72-3=0

$$27 n ^ { 2 } + 72 - 3 = 0$$

Solve for n

$$n=-\frac{\sqrt{23}i}{3}\approx -0-1.598610508i$$

$$n=\frac{\sqrt{23}i}{3}\approx 1.598610508i$$

Steps by Finding Square Root

Subtract 3 from 72 to get 69.

$$27n^{2}+69=0$$

Subtract 69 from both sides. Anything subtracted from zero gives its negation.

$$27n^{2}=-69$$

Divide both sides by 27.

$$n^{2}=\frac{-69}{27}$$

Reduce the fraction \frac{-69}{27} to lowest terms by extracting and canceling out 3.

$$n^{2}=-\frac{23}{9}$$

The equation is now solved.

$$n=\frac{\sqrt{23}i}{3} n=-\frac{\sqrt{23}i}{3}$$

Steps Using the Quadratic Formula

Subtract 3 from 72 to get 69.

$$27n^{2}+69=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 27 for a, 0 for b, and 69 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\times 27\times 69}}{2\times 27}$$

Square 0.

$$n=\frac{0±\sqrt{-4\times 27\times 69}}{2\times 27}$$

Multiply -4 times 27.

$$n=\frac{0±\sqrt{-108\times 69}}{2\times 27}$$

Multiply -108 times 69.

$$n=\frac{0±\sqrt{-7452}}{2\times 27}$$

Take the square root of -7452.

$$n=\frac{0±18\sqrt{23}i}{2\times 27}$$

Multiply 2 times 27.

$$n=\frac{0±18\sqrt{23}i}{54}$$

Now solve the equation n=\frac{0±18\sqrt{23}i}{54} when ± is plus.

$$n=\frac{\sqrt{23}i}{3}$$

Now solve the equation n=\frac{0±18\sqrt{23}i}{54} when ± is minus.

$$n=-\frac{\sqrt{23}i}{3}$$

The equation is now solved.

$$n=\frac{\sqrt{23}i}{3} n=-\frac{\sqrt{23}i}{3}$$