Let we have the following equation: $f(x)=x^2-3x+2=0$
How can I prove that $F_1(x)=\frac{x^2+2}{3}$ can be used to solve that equation with the fixed point method?
I have calculate the roots of f(x) so I know that the solutions of the equation are $x_1=1$ and $x_2=2$.
But how I make sure that $F_1(x)$ can be used for it using the fixed point method?