Hi
Newton's method consists in starting from x0, draw the tangent to the curve at the point whose abscissa is x0, find the x-intercept of this tangent x1 and so on.
You can show that
$\displaystyle x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$
Starting from x0 = 1.5 you can converge very quickly to one solution.