The method is quite easy actually, it can just be tedious because you have to do many iterations of the calculation to get a good approximation. The basic idea is that you make an initial guess of the zero, which is x_0 , or x_1 from your post. Then you use that guess to find a closer guess, x_2. Now use x_2 as your guess and you'll get x_3, etc. etc. It can take 20-30 iterations for some functions and 10ish for others, really depends on how close you want to get.