Mathematical mistakes are interesting

$ax = b \Rightarrow x = \frac{b}{a} = R$ ; $bx = a \Rightarrow x = \frac{a}{b} = r$ ; $\frac{a}{b} = \frac{1}{\frac{b}{a}} \Rightarrow r = \frac{1}{R}$ . As $r = (R - 60)$ , $(R - 60) = \frac{1}{R} \Rightarrow R^{2} - 60R - 1 = 0 \Rightarrow R = \frac{60 + \sqrt{3604}}{2} \Rightarrow R = \frac{60 + 2\sqrt{901}}{2} \Rightarrow m + \sqrt{n} = 30 + \sqrt{901} \Rightarrow m = 30$ and $n = 901 \Rightarrow \boxed{m + n = 931}$

Note : as the correct solution (R) is of the form $m + \sqrt{n}$ , I only represented the solution $R = \frac{60 + \sqrt{3604}}{2}$ , because the solution $R = \frac{60 - \sqrt{3604}}{2}$ is not the correct one.

X-1/X =60 . Find X . Where X = correct answer