To make \(k\) the subject of the formula
\begin{array}{l}
m=\frac{2 n k}{p}+\frac{k}{2 p} \\
m=\frac{4 n k+k}{2 p}
\end{array}
next. we cross - multiply
\(2 m p=4 n k+k\)
we factor out \(k\) from the R.H.S
\begin{array}{l}
2 m p=k(4 n+1) \\
\therefore k=\frac{2 m p}{4 n+1}
\end{array}