Solve c/4=9+c^2-4/6c

$$\frac { c } { 4 } = \frac { 9 + c ^ { 2 } - 4 } { 6 c }$$

Solve for c

$$c=\sqrt{10}\approx 3.16227766$$

$$c=-\sqrt{10}\approx -3.16227766$$

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 12c, the least common multiple of 4,6c.

$$3cc=2\left(9+c^{2}-4\right)$$

Multiply c and c to get c^{2}.

$$3c^{2}=2\left(9+c^{2}-4\right)$$

Subtract 4 from 9 to get 5.

$$3c^{2}=2\left(5+c^{2}\right)$$

Use the distributive property to multiply 2 by 5+c^{2}.

$$3c^{2}=10+2c^{2}$$

Subtract 2c^{2} from both sides.

$$3c^{2}-2c^{2}=10$$

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

$$c^{2}=10$$

Take the square root of both sides of the equation.

$$c=\sqrt{10} c=-\sqrt{10}$$

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 12c, the least common multiple of 4,6c.

$$3cc=2\left(9+c^{2}-4\right)$$

Multiply c and c to get c^{2}.

$$3c^{2}=2\left(9+c^{2}-4\right)$$

Subtract 4 from 9 to get 5.

$$3c^{2}=2\left(5+c^{2}\right)$$

Use the distributive property to multiply 2 by 5+c^{2}.

$$3c^{2}=10+2c^{2}$$

Subtract 10 from both sides.

$$3c^{2}-10=2c^{2}$$

Subtract 2c^{2} from both sides.

$$3c^{2}-10-2c^{2}=0$$

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

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-10\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-10\right)}}{2}$$

Multiply -4 times -10.

$$c=\frac{0±\sqrt{40}}{2}$$

Take the square root of 40.

$$c=\frac{0±2\sqrt{10}}{2}$$

Now solve the equation c=\frac{0±2\sqrt{10}}{2} when ± is plus.

$$c=\sqrt{10}$$

Now solve the equation c=\frac{0±2\sqrt{10}}{2} when ± is minus.

$$c=-\sqrt{10}$$

The equation is now solved.

$$c=\sqrt{10} c=-\sqrt{10}$$