Solve 12(18a-n)/4en-R=2R

$$\frac { 12 ( 18 a - n ) } { 4 e n - R } = 2 R$$

Solve for R

$$\left\{\begin{matrix}R=-\sqrt{6n+4\left(en\right)^{2}-108a}+2en\text{, }&\left(n>0\text{ or }a\neq \frac{n}{18}\right)\text{ and }a\leq \frac{\left(en\right)^{2}}{27}+\frac{n}{18}\\R=\sqrt{6n+4\left(en\right)^{2}-108a}+2en\text{, }&\left(n<0\text{ or }a\neq \frac{n}{18}\right)\text{ and }a\leq \frac{\left(en\right)^{2}}{27}+\frac{n}{18}\end{matrix}\right.$$

Solve for a

$$a=\frac{-R\left(R-4en\right)+6n}{108}$$

$$n\neq \frac{R}{4e}$$