Question regarding simple point iteration..

Hi guys, suppose I have the function:

3hA(T) + hB(T) = 6108.888

(where hA(T) = [Integral(0 -> T):C*dT] and C = a + b*T + c*T^2 +d*T^3

=> f(T) = 3hA(T) + hB(T) - 6108.888

In order to use the single-point iteration method, I set f(T) = 0 and added T to both sides:

Ti+1 = 3hA(Ti) + hB(Ti) - 6108.888 + Ti

I've set as a starting value of the iteration T0 = 500

The problem is, I can't get the function to converge.

The Newton-Raphson method(using T=500 as well) as well as the bisection method (with values 500,1100) converge and give me a root estimation of ~679.

I tried using (Ti+1)^2 = (3hA(Ti) + hB(Ti) - 6108.888 + Ti)^2 but still nothing.

Is there a way to make it converge ?

Regards