Solve F=1/4piepsilon_{0R^2}

$$F = \frac { 1 } { 4 \pi \epsilon _ { 0 } R ^ { 2 } }$$

Solve for R (complex solution)

$$R=-\frac{ϵ_{0}^{-\frac{1}{2}}\left(\pi F\right)^{-\frac{1}{2}}}{2}$$

$$R=\frac{ϵ_{0}^{-\frac{1}{2}}\left(\pi F\right)^{-\frac{1}{2}}}{2}\text{, }F\neq 0\text{ and }ϵ_{0}\neq 0$$

Solve for F

$$F=\frac{1}{4\pi ϵ_{0}R^{2}}$$

$$R\neq 0\text{ and }ϵ_{0}\neq 0$$

Solve for R

$$R=\frac{1}{2\sqrt{\pi Fϵ_{0}}}$$

$$R=-\frac{1}{2\sqrt{\pi Fϵ_{0}}}\text{, }\left(ϵ_{0}>0\text{ and }F>0\right)\text{ or }\left(F<0\text{ and }ϵ_{0}<0\right)$$