I assume you are familiar with the method itself, here is how you apply it to this problem.

To approximate the intersection of two curves, you can use Newton's method to approximate the root(s) of their difference.

That is, if the two curves are and , then solving for their intersection points requires finding all x-values such that which is the same as solving for .

So let . We can use Newton's method to approximate the zeros of , which will be the x-values for our intersection points. Got it?

Also see: Newton's method - Wikipedia