Solve f-k/2pi=sqrt{LC}

$$\frac { f - k } { 2 \pi } = \sqrt { L C }$$

Solve for C

$$\left\{\begin{matrix}C=\frac{\left(\frac{f-k}{\pi }\right)^{2}}{4L}\text{, }&f\geq k\text{ and }L\neq 0\\C\in \mathrm{R}\text{, }&f=k\text{ and }L=0\end{matrix}\right.$$

Steps for Solving Radical Equations

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{LC}=\frac{f-k}{2\pi }$$

Square both sides of the equation.

$$LC=\frac{\left(f-k\right)^{2}}{4\pi ^{2}}$$

Divide both sides by L.

$$\frac{LC}{L}=\frac{\left(f-k\right)^{2}}{4\pi ^{2}L}$$

Dividing by L undoes the multiplication by L.

$$C=\frac{\left(f-k\right)^{2}}{4\pi ^{2}L}$$

Solve for L

$$\left\{\begin{matrix}L=\frac{\left(\frac{f-k}{\pi }\right)^{2}}{4C}\text{, }&f\geq k\text{ and }C\neq 0\\L\in \mathrm{R}\text{, }&f=k\text{ and }C=0\end{matrix}\right.$$

Steps for Solving Radical Equations

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{LC}=\frac{f-k}{2\pi }$$

Square both sides of the equation.

$$CL=\frac{\left(f-k\right)^{2}}{4\pi ^{2}}$$

Divide both sides by C.

$$\frac{CL}{C}=\frac{\left(f-k\right)^{2}}{4\pi ^{2}C}$$

Dividing by C undoes the multiplication by C.

$$L=\frac{\left(f-k\right)^{2}}{4\pi ^{2}C}$$

Solve for C (complex solution)

$$\left\{\begin{matrix}C=\frac{\left(\frac{f-k}{\pi }\right)^{2}}{4L}\text{, }&L\neq 0\text{ and }\left(f=k\text{ or }arg(f-k)<\pi \right)\\C\in \mathrm{C}\text{, }&f=k\text{ and }L=0\end{matrix}\right.$$

Solve for L (complex solution)

$$\left\{\begin{matrix}L=\frac{\left(\frac{f-k}{\pi }\right)^{2}}{4C}\text{, }&C\neq 0\text{ and }\left(f=k\text{ or }arg(f-k)<\pi \right)\\L\in \mathrm{C}\text{, }&f=k\text{ and }C=0\end{matrix}\right.$$