It has been a long time since I last used one of those fancy HP calculators. As I recall, the equation solver built into the calculator simply used a Newton-Raphson algorithm to find the root(s) of the given equation. Because Solver also uses the NR algorithm, I see no reason why you can't program this in Excel.

I'm not certain at this point what your question really is. What do you mean by it "restricts me to one answer" and "I need to have seven solvers running"? A sample file might be useful for illustrating your current solution to the problem to show where it is not working and what you want it to do so that it works for you.