Solve 3a^2+12=5

$$3 a ^ { 2 } + 12 = 5$$

Solve for a

$$a=-\frac{\sqrt{21}i}{3}\approx -0-1.527525232i$$

$$a=\frac{\sqrt{21}i}{3}\approx 1.527525232i$$

Steps by Finding Square Root

Subtract 12 from both sides.

$$3a^{2}=5-12$$

Subtract 12 from 5 to get -7.

$$3a^{2}=-7$$

Divide both sides by 3.

$$a^{2}=-\frac{7}{3}$$

The equation is now solved.

$$a=\frac{\sqrt{21}i}{3} a=-\frac{\sqrt{21}i}{3}$$

Steps Using the Quadratic Formula

Subtract 5 from both sides.

$$3a^{2}+12-5=0$$

Subtract 5 from 12 to get 7.

$$3a^{2}+7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and 7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 3\times 7}}{2\times 3}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 3\times 7}}{2\times 3}$$

Multiply -4 times 3.

$$a=\frac{0±\sqrt{-12\times 7}}{2\times 3}$$

Multiply -12 times 7.

$$a=\frac{0±\sqrt{-84}}{2\times 3}$$

Take the square root of -84.

$$a=\frac{0±2\sqrt{21}i}{2\times 3}$$

Multiply 2 times 3.

$$a=\frac{0±2\sqrt{21}i}{6}$$

Now solve the equation a=\frac{0±2\sqrt{21}i}{6} when ± is plus.

$$a=\frac{\sqrt{21}i}{3}$$

Now solve the equation a=\frac{0±2\sqrt{21}i}{6} when ± is minus.

$$a=-\frac{\sqrt{21}i}{3}$$

The equation is now solved.

$$a=\frac{\sqrt{21}i}{3} a=-\frac{\sqrt{21}i}{3}$$