Solving $\binom{39}{5+2x}=\binom{39}{2x-2}$ I have this equation: $$\binom{39}{5+2x}=\binom{39}{2x-2}$$
And I don't know how to solve it. I've tried by the definition of combination but I get stuck.
I get stuck here:

we have
$\binom{n}{p}=\binom{n}{n-p}$
so your equation offers two possibilities:
$5+2x=2x-2$ which is not possible
or
$5+2x=39-(2x-2) $  which gives
$x=\frac{36}{4}=9$.
