Name of the numerical method I came across one numerical method, however I have lost the link or is not able to find it on my history.
It used the following variables:
$$G=\frac{p'(x_k)}{p(x_k)} \ \& \ \ H=G^2-\frac{p''(x_k)}{p(x_k)}$$
Or something to that effect, not entirely sure. Thanks in advance!

That looks like part of the Laguerre method for polynomial roots.
$$
x_{k+1}=x_k-\frac{n}{G\pm\sqrt{(n-1)(nH-G^2)}}.
$$
