Solve 12/3a^2+2=3

$$\frac { 12 } { 3 a ^ { 2 } + 2 } = 3$$

Solve for a

$$a=\frac{\sqrt{6}}{3}\approx 0.816496581$$

$$a=-\frac{\sqrt{6}}{3}\approx -0.816496581$$

Steps by Finding Square Root

Multiply both sides of the equation by 3a^{2}+2.

$$12=3\left(3a^{2}+2\right)$$

Use the distributive property to multiply 3 by 3a^{2}+2.

$$12=9a^{2}+6$$

Swap sides so that all variable terms are on the left hand side.

$$9a^{2}+6=12$$

Subtract 6 from both sides.

$$9a^{2}=12-6$$

Subtract 6 from 12 to get 6.

$$9a^{2}=6$$

Divide both sides by 9.

$$a^{2}=\frac{6}{9}$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

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

Take the square root of both sides of the equation.

$$a=\frac{\sqrt{6}}{3} a=-\frac{\sqrt{6}}{3}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 3a^{2}+2.

$$12=3\left(3a^{2}+2\right)$$

Use the distributive property to multiply 3 by 3a^{2}+2.

$$12=9a^{2}+6$$

Swap sides so that all variable terms are on the left hand side.

$$9a^{2}+6=12$$

Subtract 12 from both sides.

$$9a^{2}+6-12=0$$

Subtract 12 from 6 to get -6.

$$9a^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 9\left(-6\right)}}{2\times 9}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 9\left(-6\right)}}{2\times 9}$$

Multiply -4 times 9.

$$a=\frac{0±\sqrt{-36\left(-6\right)}}{2\times 9}$$

Multiply -36 times -6.

$$a=\frac{0±\sqrt{216}}{2\times 9}$$

Take the square root of 216.

$$a=\frac{0±6\sqrt{6}}{2\times 9}$$

Multiply 2 times 9.

$$a=\frac{0±6\sqrt{6}}{18}$$

Now solve the equation a=\frac{0±6\sqrt{6}}{18} when ± is plus.

$$a=\frac{\sqrt{6}}{3}$$

Now solve the equation a=\frac{0±6\sqrt{6}}{18} when ± is minus.

$$a=-\frac{\sqrt{6}}{3}$$

The equation is now solved.

$$a=\frac{\sqrt{6}}{3} a=-\frac{\sqrt{6}}{3}$$