How to find the common difference in this case?

Question

The first and the last terms of an A.P. are $ a$ and $l $ respectively. If $S $ be the sum of the terms, then show that the common difference is $$\frac {l^2 -a^2}{2S -(l + a)} $$

Answer 1

I figured it out:

$ l = a + (n -1) d $ $Or, \; d=\frac {l-a}{n-1} $ $ Or, \; d= \frac {(l-a)(l+a)}{(n-1)(l+a)} $ $ Or, \; d= \frac {l^2 -a^2}{n(l+a) - (l+a)} $ $ Or, \; d= \frac {l^2 -a^2}{2S - (l+a)} $ (as $S = \frac {n}{2} ( a+l) $)

A special thanks to @dxiv