Let H be a Hilbert space, X be a real Banach space, A : H longrightarrow X be an operator with D(A) dense in H, G： H longrightarrow H be positive definite, $chi$ $in$ D(A) and b $in$ H. Consider the quadratic programming problem: QP： Minimize $frac{1}{2}$〈p, $chi$〉 + 〈$chi$, G$chi$〉 subject to A$chi$= b In this paper, we obtain an explicit solution to the above problem using generalized inverses.