This paper presents real power optimization with load flow using an adaptive Hopfield neural network. in order to speed up the convergence of the Hopfield neural network system, the two adaptive methods, slope adjustment and bias adjustment, were used with adaptive learning rates. Algorithms of economic load dispatch for piecewise quadratic cost functions using the Hopfield neural network have been developed for the two approaches. Instead of using the typical B-coefficient method, this paper uses actual load flow to compute the transmission loss accurately. These methods for optimization has been tested in the IEEE 30-bus system to demonstrate its effectiveness. The performance of the proposed approaches is evaluated by comparing the results of the slope adjustment and the bias adjustment methods with those of the conventional Hopfield network, and an additional improvement was demonstrated by the use of momentum in the adaptive learning approaches.