Solve z^2-y9z-100=0

$$z ^ { 2 } - y 9 z - 100 = 0$$

Solve for y_9

$$y_{9}=z-\frac{100}{z}$$

$$z\neq 0$$

Steps for Solving Linear Equation

Subtract z^{2} from both sides. Anything subtracted from zero gives its negation.

$$-y_{9}z-100=-z^{2}$$

Add 100 to both sides.

$$-y_{9}z=-z^{2}+100$$

The equation is in standard form.

$$\left(-z\right)y_{9}=100-z^{2}$$

Divide both sides by -z.

$$\frac{\left(-z\right)y_{9}}{-z}=\frac{100-z^{2}}{-z}$$

Dividing by -z undoes the multiplication by -z.

$$y_{9}=\frac{100-z^{2}}{-z}$$

Divide -z^{2}+100 by -z.

$$y_{9}=z-\frac{100}{z}$$

Solve for z

$$z=\frac{\sqrt{y_{9}^{2}+400}+y_{9}}{2}$$

$$z=\frac{-\sqrt{y_{9}^{2}+400}+y_{9}}{2}$$