Solve 6w^2-13=15-3w^2

$$6 w ^ { 2 } - 13 = 15 - 3 w ^ { 2 }$$

Solve for w

$$w = \frac{2 \sqrt{7}}{3} \approx 1.763834207$$

$$w = -\frac{2 \sqrt{7}}{3} \approx -1.763834207$$

Steps by Finding Square Root

Add 3w^{2} to both sides.

$$6w^{2}-13+3w^{2}=15$$

Combine 6w^{2} and 3w^{2} to get 9w^{2}.

$$9w^{2}-13=15$$

Add 13 to both sides.

$$9w^{2}=15+13$$

Add 15 and 13 to get 28.

$$9w^{2}=28$$

Divide both sides by 9.

$$w^{2}=\frac{28}{9}$$

Take the square root of both sides of the equation.

$$w=\frac{2\sqrt{7}}{3} w=-\frac{2\sqrt{7}}{3}$$

Steps Using the Quadratic Formula

Subtract 15 from both sides.

$$6w^{2}-13-15=-3w^{2}$$

Subtract 15 from -13 to get -28.

$$6w^{2}-28=-3w^{2}$$

Add 3w^{2} to both sides.

$$6w^{2}-28+3w^{2}=0$$

Combine 6w^{2} and 3w^{2} to get 9w^{2}.

$$9w^{2}-28=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and -28 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{0±\sqrt{0^{2}-4\times 9\left(-28\right)}}{2\times 9}$$

Square 0.

$$w=\frac{0±\sqrt{-4\times 9\left(-28\right)}}{2\times 9}$$

Multiply -4 times 9.

$$w=\frac{0±\sqrt{-36\left(-28\right)}}{2\times 9}$$

Multiply -36 times -28.

$$w=\frac{0±\sqrt{1008}}{2\times 9}$$

Take the square root of 1008.

$$w=\frac{0±12\sqrt{7}}{2\times 9}$$

Multiply 2 times 9.

$$w=\frac{0±12\sqrt{7}}{18}$$

Now solve the equation w=\frac{0±12\sqrt{7}}{18} when ± is plus.

$$w=\frac{2\sqrt{7}}{3}$$

Now solve the equation w=\frac{0±12\sqrt{7}}{18} when ± is minus.

$$w=-\frac{2\sqrt{7}}{3}$$

The equation is now solved.

$$w=\frac{2\sqrt{7}}{3} w=-\frac{2\sqrt{7}}{3}$$