This paper investigates the application of quantum computing, specifically the Harrow-Hassidim-Lloyd (HHL) algorithm, to solve quadratic programming problems with equality constraints (QPE), which have wide-ranging applications across various fields. Notably, QPE problems arise as subproblems in non-linear optimization, where methods like sequential quadratic programming (SQP) address non-linear problems by transforming them into a sequence of QPE problems. To our knowledge, QPE problems have not been explored in the existing quantum optimization literature. In the proposed approach, the QPE problem is reformulated as a linear equation system, making it possible to apply quantum algorithms such as HHL for its solution. Case studies demonstrate that even simple and sparse QPE problems can result in computationally expensive steps within the HHL algorithm. Moreover, the distribution of eigenvalues in the linear equation system significantly affects the number of qubits required to achieve a solution with the desired level of precision. These findings highlight the challenges of applying quantum computing to general QP problems and underscore the need for further studies to refine this approach.