Solve 3a^2=a^2+4

$$3 a ^ { 2 } = a ^ { 2 } + 4$$

Solve for a

$$a=\sqrt{2}\approx 1.414213562$$

$$a=-\sqrt{2}\approx -1.414213562$$

Steps by Finding Square Root

Subtract a^{2} from both sides.

$$3a^{2}-a^{2}=4$$

Combine 3a^{2} and -a^{2} to get 2a^{2}.

$$2a^{2}=4$$

Divide both sides by 2.

$$a^{2}=\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$a^{2}=2$$

Take the square root of both sides of the equation.

$$a=\sqrt{2} a=-\sqrt{2}$$

Steps Using the Quadratic Formula

Subtract a^{2} from both sides.

$$3a^{2}-a^{2}=4$$

Combine 3a^{2} and -a^{2} to get 2a^{2}.

$$2a^{2}=4$$

Subtract 4 from both sides.

$$2a^{2}-4=0$$

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

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

Square 0.

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

Multiply -4 times 2.

$$a=\frac{0±\sqrt{-8\left(-4\right)}}{2\times 2}$$

Multiply -8 times -4.

$$a=\frac{0±\sqrt{32}}{2\times 2}$$

Take the square root of 32.

$$a=\frac{0±4\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$a=\frac{0±4\sqrt{2}}{4}$$

Now solve the equation a=\frac{0±4\sqrt{2}}{4} when ± is plus.

$$a=\sqrt{2}$$

Now solve the equation a=\frac{0±4\sqrt{2}}{4} when ± is minus.

$$a=-\sqrt{2}$$

The equation is now solved.

$$a=\sqrt{2} a=-\sqrt{2}$$