Solve 5c^2-36/4c^2=1/2

$$\frac { 5 c ^ { 2 } - 36 } { 4 c ^ { 2 } } = \frac { 1 } { 2 }$$

Solve for c

$$c=2\sqrt{3}\approx 3.464101615$$

$$c=-2\sqrt{3}\approx -3.464101615$$

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 4c^{2}, the least common multiple of 4c^{2},2.

$$5c^{2}-36=2c^{2}$$

Subtract 2c^{2} from both sides.

$$5c^{2}-36-2c^{2}=0$$

Combine 5c^{2} and -2c^{2} to get 3c^{2}.

$$3c^{2}-36=0$$

Add 36 to both sides. Anything plus zero gives itself.

$$3c^{2}=36$$

Divide both sides by 3.

$$c^{2}=\frac{36}{3}$$

Divide 36 by 3 to get 12.

$$c^{2}=12$$

Take the square root of both sides of the equation.

$$c=2\sqrt{3} c=-2\sqrt{3}$$

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 4c^{2}, the least common multiple of 4c^{2},2.

$$5c^{2}-36=2c^{2}$$

Subtract 2c^{2} from both sides.

$$5c^{2}-36-2c^{2}=0$$

Combine 5c^{2} and -2c^{2} to get 3c^{2}.

$$3c^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\times 3\left(-36\right)}}{2\times 3}$$

Square 0.

$$c=\frac{0±\sqrt{-4\times 3\left(-36\right)}}{2\times 3}$$

Multiply -4 times 3.

$$c=\frac{0±\sqrt{-12\left(-36\right)}}{2\times 3}$$

Multiply -12 times -36.

$$c=\frac{0±\sqrt{432}}{2\times 3}$$

Take the square root of 432.

$$c=\frac{0±12\sqrt{3}}{2\times 3}$$

Multiply 2 times 3.

$$c=\frac{0±12\sqrt{3}}{6}$$

Now solve the equation c=\frac{0±12\sqrt{3}}{6} when ± is plus.

$$c=2\sqrt{3}$$

Now solve the equation c=\frac{0±12\sqrt{3}}{6} when ± is minus.

$$c=-2\sqrt{3}$$

The equation is now solved.

$$c=2\sqrt{3} c=-2\sqrt{3}$$