yeah, I think newton method is a better solver.
e.g f(x)=5*x^2+sin(x)
find the x values such that f(x)=0
you can guess one initial x0 value
calculate f(x0) and the differntial f'(x0) values
let d=-f/f'
x=x+d
loop until the abs(d)< a small number
that's done!