Any help would be greatly appreciated.
Correct, but it is not a good idea to use "a" to represent two different quantities!
Perhaps it would be better to write
"The roots to the equation $\displaystyle ix^2+ jx+ k= 0$ are $\displaystyle x= \frac{-j\pm\sqrt{j^2- 4ik}}{2i}$. For this problem, i= 1, j= (a-1)/a, k= -1".
(I am assuming that in the first post, "a- 1/a" meant "(a-1)/a", not "a- (1/a)".)
This quadratic factorises as $\displaystyle (x+a)(x-\tfrac1a)$. So the solutions of the equation are $\displaystyle x=-a$ and $\displaystyle x-\tfrac1a$.
(I am making the opposite assumption from HallsofIvy, namely that, "a- 1/a" meant "a- (1/a)", not "(a-1)/a".)