Solve z/5-1/z=z/6

$$\frac { z } { 5 } - \frac { 1 } { z } = \frac { z } { 6 }$$

Solve for z

$$z=\sqrt{30}\approx 5.477225575$$

$$z=-\sqrt{30}\approx -5.477225575$$

Steps by Finding Square Root

Variable z cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 30z, the least common multiple of 5,z,6.

$$6zz-30=5zz$$

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

$$6z^{2}-30=5zz$$

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

$$6z^{2}-30=5z^{2}$$

Subtract 5z^{2} from both sides.

$$6z^{2}-30-5z^{2}=0$$

Combine 6z^{2} and -5z^{2} to get z^{2}.

$$z^{2}-30=0$$

Add 30 to both sides. Anything plus zero gives itself.

$$z^{2}=30$$

Take the square root of both sides of the equation.

$$z=\sqrt{30} z=-\sqrt{30}$$

Steps Using the Quadratic Formula

Variable z cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 30z, the least common multiple of 5,z,6.

$$6zz-30=5zz$$

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

$$6z^{2}-30=5zz$$

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

$$6z^{2}-30=5z^{2}$$

Subtract 5z^{2} from both sides.

$$6z^{2}-30-5z^{2}=0$$

Combine 6z^{2} and -5z^{2} to get z^{2}.

$$z^{2}-30=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -30 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\left(-30\right)}}{2}$$

Square 0.

$$z=\frac{0±\sqrt{-4\left(-30\right)}}{2}$$

Multiply -4 times -30.

$$z=\frac{0±\sqrt{120}}{2}$$

Take the square root of 120.

$$z=\frac{0±2\sqrt{30}}{2}$$

Now solve the equation z=\frac{0±2\sqrt{30}}{2} when ± is plus.

$$z=\sqrt{30}$$

Now solve the equation z=\frac{0±2\sqrt{30}}{2} when ± is minus.

$$z=-\sqrt{30}$$

The equation is now solved.

$$z=\sqrt{30} z=-\sqrt{30}$$