How can I find all solutions using an iteration formula? Take the equation $x^2+7x+10=0$, which has roots $-2$ and $-5$. 
When I use the iteration formula $x_{n+1}=\dfrac{-10}{x_n+7}$, I always converge on $-2$ but not on $-5$. 
I have tried starting values of $-6, -4, -1, 1, 2$ and many others, but I only converge on $-2$. 
Is there something wrong with my iteration formula or starting values?

An iterative formula is not a 100% sure method of finding a solution. This is a method based on approximation. 
The kind of iteration you are using is a fixed point iteration. It will only work with attractive points, not repulsive points.
