This paper investigates the quadratic convex optimization problem with equality constraint for multi-agent systems (MASs). In order to reduce the controllers' update frequency and the communication burden among agents, a distributed event-triggered optimization algorithm is proposed. Based on the graph theorem and Lyapunov function method, two different event-triggered conditions are designed, which guarantee that agents can asymptotically converge to their optimal values. Especially, the second event-triggered condition dose not require the information of the largest eigenvalue of the Laplacian matrix, and thus the algorithm can be implemented in a fully distributed way. The continuous update of controllers and the continuous communication among agents are not required. Meanwhile, the interval of any two contiguous event trigger instants of each agent is more than zero, and continuous event triggering is avoided. Finally, the proposed algorithm is verified in the Matlab simulation environment, and the result of numerical simulation shows the effectiveness of the proposed algorithm.