Solve 84=3w^2

$$84 = 3 w ^ { 2 }$$

Solve for w

$$w=2\sqrt{7}\approx 5.291502622$$

$$w=-2\sqrt{7}\approx -5.291502622$$

Steps by Finding Square Root

Divide both sides by 3.

$$\frac{84}{3}=w^{2}$$

Divide 84 by 3 to get 28.

$$28=w^{2}$$

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

$$w^{2}=28$$

Take the square root of both sides of the equation.

$$w=2\sqrt{7} w=-2\sqrt{7}$$

Steps Using the Quadratic Formula

Divide both sides by 3.

$$\frac{84}{3}=w^{2}$$

Divide 84 by 3 to get 28.

$$28=w^{2}$$

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

$$w^{2}=28$$

Subtract 28 from both sides.

$$w^{2}-28=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -28 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{0±\sqrt{0^{2}-4\left(-28\right)}}{2}$$

Square 0.

$$w=\frac{0±\sqrt{-4\left(-28\right)}}{2}$$

Multiply -4 times -28.

$$w=\frac{0±\sqrt{112}}{2}$$

Take the square root of 112.

$$w=\frac{0±4\sqrt{7}}{2}$$

Now solve the equation w=\frac{0±4\sqrt{7}}{2} when ± is plus.

$$w=2\sqrt{7}$$

Now solve the equation w=\frac{0±4\sqrt{7}}{2} when ± is minus.

$$w=-2\sqrt{7}$$

The equation is now solved.

$$w=2\sqrt{7} w=-2\sqrt{7}$$