Solve 10c^2-2/6c^2=2/3

$$\frac { 10 c ^ { 2 } - 2 } { 6 c ^ { 2 } } = \frac { 2 } { 3 }$$

Solve for c

$$c=\frac{\sqrt{3}}{3}\approx 0.577350269$$

$$c=-\frac{\sqrt{3}}{3}\approx -0.577350269$$

Steps by Finding Square Root

Variable c cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6c^{2}, the least common multiple of 6c^{2},3.

$$10c^{2}-2=4c^{2}$$

Subtract 4c^{2} from both sides.

$$10c^{2}-2-4c^{2}=0$$

Combine 10c^{2} and -4c^{2} to get 6c^{2}.

$$6c^{2}-2=0$$

Add 2 to both sides. Anything plus zero gives itself.

$$6c^{2}=2$$

Divide both sides by 6.

$$c^{2}=\frac{2}{6}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$c^{2}=\frac{1}{3}$$

Take the square root of both sides of the equation.

$$c=\frac{\sqrt{3}}{3} c=-\frac{\sqrt{3}}{3}$$

Steps Using the Quadratic Formula

Variable c cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6c^{2}, the least common multiple of 6c^{2},3.

$$10c^{2}-2=4c^{2}$$

Subtract 4c^{2} from both sides.

$$10c^{2}-2-4c^{2}=0$$

Combine 10c^{2} and -4c^{2} to get 6c^{2}.

$$6c^{2}-2=0$$

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

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

Square 0.

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

Multiply -4 times 6.

$$c=\frac{0±\sqrt{-24\left(-2\right)}}{2\times 6}$$

Multiply -24 times -2.

$$c=\frac{0±\sqrt{48}}{2\times 6}$$

Take the square root of 48.

$$c=\frac{0±4\sqrt{3}}{2\times 6}$$

Multiply 2 times 6.

$$c=\frac{0±4\sqrt{3}}{12}$$

Now solve the equation c=\frac{0±4\sqrt{3}}{12} when ± is plus.

$$c=\frac{\sqrt{3}}{3}$$

Now solve the equation c=\frac{0±4\sqrt{3}}{12} when ± is minus.

$$c=-\frac{\sqrt{3}}{3}$$

The equation is now solved.

$$c=\frac{\sqrt{3}}{3} c=-\frac{\sqrt{3}}{3}$$