Solve h_{z}=b+delta/2/L-1

$$h _ { z } = \frac { b + \delta / 2 } { L - 1 }$$

Solve for L

$$\left\{\begin{matrix}L=\frac{2b+2h_{z}+\delta }{2h_{z}}\text{, }&b\neq -\frac{\delta }{2}\text{ and }h_{z}\neq 0\\L\neq 1\text{, }&h_{z}=0\text{ and }b=-\frac{\delta }{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable L cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by L-1.

$$h_{z}\left(L-1\right)=b+\frac{\delta }{2}$$

Use the distributive property to multiply h_{z} by L-1.

$$h_{z}L-h_{z}=b+\frac{\delta }{2}$$

Add h_{z} to both sides.

$$h_{z}L=b+\frac{\delta }{2}+h_{z}$$

Multiply both sides of the equation by 2.

$$2h_{z}L=2b+\delta +2h_{z}$$

The equation is in standard form.

$$2h_{z}L=2b+2h_{z}+\delta$$

Divide both sides by 2h_{z}.

$$\frac{2h_{z}L}{2h_{z}}=\frac{2b+2h_{z}+\delta }{2h_{z}}$$

Dividing by 2h_{z} undoes the multiplication by 2h_{z}.

$$L=\frac{2b+2h_{z}+\delta }{2h_{z}}$$

Divide 2b+\delta +2h_{z} by 2h_{z}.

$$L=\frac{\frac{\delta }{2}+b}{h_{z}}+1$$

Variable L cannot be equal to 1.

$$L=\frac{\frac{\delta }{2}+b}{h_{z}}+1\text{, }L\neq 1$$

Solve for b

$$b=Lh_{z}-\frac{\delta }{2}-h_{z}$$

$$L\neq 1$$