My formulas are:
I would like to solve for a where they touch (exact solution).
Here is a graph demonstrating what I mean:
As you can see, I have attempted to solve for a by making them closer and closer.
I think 1.100917368760402698 ≤ a ≤ 1.100917368760402699, but floating point error may have reduced the accuracy of that range, but it should be near those numbers at least.
There will also be a negative solution of a, which will be exactly negative I believe.