Solve 16=3x^2

$$16=3 { x }^{ 2 }$$

Solve for x

$$x = \frac{4 \sqrt{3}}{3} \approx 2.309401077$$

$$x = -\frac{4 \sqrt{3}}{3} \approx -2.309401077$$

Steps by Finding Square Root

Divide both sides by 3.

$$\frac{16}{3}=x^{2}$$

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

$$x^{2}=\frac{16}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{3}}{3} x=-\frac{4\sqrt{3}}{3}$$

Steps Using the Quadratic Formula

Divide both sides by 3.

$$\frac{16}{3}=x^{2}$$

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

$$x^{2}=\frac{16}{3}$$

Subtract \frac{16}{3} from both sides.

$$x^{2}-\frac{16}{3}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{16}{3} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{16}{3}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{16}{3}\right)}}{2}$$

Multiply -4 times -\frac{16}{3}.

$$x=\frac{0±\sqrt{\frac{64}{3}}}{2}$$

Take the square root of \frac{64}{3}.

$$x=\frac{0±\frac{8\sqrt{3}}{3}}{2}$$

Now solve the equation x=\frac{0±\frac{8\sqrt{3}}{3}}{2} when ± is plus.

$$x=\frac{4\sqrt{3}}{3}$$

Now solve the equation x=\frac{0±\frac{8\sqrt{3}}{3}}{2} when ± is minus.

$$x=-\frac{4\sqrt{3}}{3}$$

The equation is now solved.

$$x=\frac{4\sqrt{3}}{3} x=-\frac{4\sqrt{3}}{3}$$