Ok so Newton's method is a way of determining a root of the equation
in both of the cases above for we obtain so we just need to apply Newton's method.
This works by calculating the tangent line at a point finding where it intersects the x-axis and assuming that this gives a better approximation to the root than
Graphically you can see it at work here
Algebraically it is
A derivation can be found here Newton's method - Wikipedia, the free encyclopedia
So work out the derivatives of the two functions you have above then plug it into the formula and you should have two iterative formulas which will converge on