Fixed point iteration
The equation can be solved with fixed point iteration by rearranging into the form and calculating successive iterates from that. When students first see this method there seems to be no obvious pattern about which rearrangements or starting values will converge to a solution.
Fixed point iteration can be shown graphically, with the solution to the equation being the intersection of and . The resulting patterns show convergence or divergence (and described as 'staircase' or 'cobweb', depending on the shape).
Leave and change in the window to suit the equation you are solving.
(This is a work in progress; I'll update the user interface to this when I get time).