I want just how to solve it give me a hint

The question:-

Use fixed-point iteration method to determine a solution accurate to within for on [1,2] use

here is my solution (correct me if I was wrong )

first we should dtermine F(x)=x so

so F(x) is converge now

..................etc

when I should stop ??

my solution is correct or it is wrong ??

Thanks for the help