Solve 3u^2+2=0

$$3 u ^ { 2 } + 2 = 0$$

Solve for u

$$u=-\frac{\sqrt{6}i}{3}\approx -0-0.816496581i$$

$$u=\frac{\sqrt{6}i}{3}\approx 0.816496581i$$

Steps by Finding Square Root

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$3u^{2}=-2$$

Divide both sides by 3.

$$u^{2}=-\frac{2}{3}$$

The equation is now solved.

$$u=\frac{\sqrt{6}i}{3} u=-\frac{\sqrt{6}i}{3}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$3u^{2}+2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and 2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$u=\frac{0±\sqrt{0^{2}-4\times 3\times 2}}{2\times 3}$$

Square 0.

$$u=\frac{0±\sqrt{-4\times 3\times 2}}{2\times 3}$$

Multiply -4 times 3.

$$u=\frac{0±\sqrt{-12\times 2}}{2\times 3}$$

Multiply -12 times 2.

$$u=\frac{0±\sqrt{-24}}{2\times 3}$$

Take the square root of -24.

$$u=\frac{0±2\sqrt{6}i}{2\times 3}$$

Multiply 2 times 3.

$$u=\frac{0±2\sqrt{6}i}{6}$$

Now solve the equation u=\frac{0±2\sqrt{6}i}{6} when ± is plus.

$$u=\frac{\sqrt{6}i}{3}$$

Now solve the equation u=\frac{0±2\sqrt{6}i}{6} when ± is minus.

$$u=-\frac{\sqrt{6}i}{3}$$

The equation is now solved.

$$u=\frac{\sqrt{6}i}{3} u=-\frac{\sqrt{6}i}{3}$$