Newton's method is numerical method for solving nonlinear equations of type `f(x)=0.` If you have `n`-th approximation you can calculate `(n+1)`-st approximation using the formula:

`x_(n+1)=x_n-(f(x_n))/(f'(x_n)).`

For further explenation see the link below.

Lets calculate derivation: `f'(x)=5x^4-1.` So you have:

`x_2 = 2 - (24)/(79) = 1.6962`

`x_3 = 1.6962 - (6.34439)/(40.38836) = 1.53912` 

Your final solution would be something like `x_n = 1.49612.` Of course that's only one of 5 solutions to this equation. Other 4 solutions are complex numbers. If you want to get complex solutions, your initial approximation must be complex.