Solve frac{R_{11}}{R_{12}}=lnd+2delta/d/2delta/d

$$\frac { R _ { 11 } } { R _ { 12 } } = \frac { \ln \frac { d + 2 \delta } { d } } { 2 \delta / d }$$

Solve for R_11 (complex solution)

$$R_{11}=\frac{\ln(\frac{d+2\delta }{d})R_{12}d}{2\delta }$$

$$\delta \neq 0\text{ and }d\neq -2\delta \text{ and }d\neq 0\text{ and }R_{12}\neq 0$$

Solve for R_12 (complex solution)

$$R_{12}=\frac{2R_{11}\delta }{\ln(\frac{d+2\delta }{d})d}$$

$$\delta \neq 0\text{ and }R_{11}\neq 0\text{ and }d\neq -2\delta \text{ and }d\neq 0$$

Solve for R_11

$$R_{11}=\frac{\ln(\frac{d+2\delta }{d})R_{12}d}{2\delta }$$

$$\left(\delta \neq 0\text{ and }d>-2\delta \text{ and }d>0\text{ and }R_{12}\neq 0\right)\text{ or }\left(\delta \neq 0\text{ and }d<-2\delta \text{ and }d<0\text{ and }R_{12}\neq 0\right)$$

Solve for R_12

$$R_{12}=\frac{2R_{11}\delta }{\ln(\frac{d+2\delta }{d})d}$$

$$\left(\delta \neq 0\text{ and }R_{11}\neq 0\text{ and }d<-2\delta \text{ and }d<0\right)\text{ or }\left(\delta \neq 0\text{ and }R_{11}\neq 0\text{ and }d>-2\delta \text{ and }d>0\right)$$