I've spent quite a bit of time searching for an answer to my problem, but one of the main problems is that I don't exactly know how to phrase it correctly.
I have an equation in two variable that I want to find the roots in one variable (E) as a function of the other(r). I can plot f(E) with a known r relatively fast, but I cannot find the roots at all. I've tried Solve, FindRoot, and FindInstance with various accuracy and precision goals and damping factors. I think one of the main problems is that the numbers involved are quite large. I only care about two or three sig figs, but even at the lowest precision, mathematica wants the accuracy to be to the right of the decimal place, which gives about 15 significant figures. I also think there is a small imaginary component to the solution that I don't care about, but may be preventing the calculation from converging.
Basically, I want a rough, fast estimate of the zeros. I could do it by hand, but it seems to me that if the computer can plot the function as rapidly as it does, I should be able to set the tolerances where I want and get an idea of where the zero is.