Solve for r.

f/(r ^ 2) + a = n + k

f/(r ^ 2) = n + k - a after subtracting 'a' from both sides of the equation

f/(n+k-a) = r^2 after re-arranging now take sqrt of both sides

r = +- sqrt ( f/(n+k-a) ) (and as WIJ pointed out n+k-a cannot equal 0)

\(r=\sqrt{\frac{f}{n+k-a}}, r=-\sqrt{\frac{f}{n+k-a}};\quad \:a\ne \:n+k\)