We consider the exact solution of Problem $\QP$ which consists in minimizing a quadratic function subject to quadratic constraints. We start with an explicit description of new general triangle inequalities that are derived from the ranges of the variables of $\QP$. We show that they extend the triangle inequalities, introduced for the binary case, to variables that belong to a generic interval. We also prove that these inequalities cut feasible solutions of McCormick envelopes, and we relate them to the literature. We then introduce $(SDP)$, a strong semidefinite relaxation of $\QP$, that we call ``Shor's plus RLT plus Triangle'', which includes both the McCormick envelopes and the general triangle inequalities. We further show how to compute a convex relaxation $(P^*)$ whose optimal value reaches the value of $(SDP)$. In order to handle these inequalities in the solution of $(SDP)$, we solve it by a heuristic that also serves as a separation algorithm. We then solve $\QP$ to global optimality with a \bb~based on $(P^*)$. Finally, we show that our method outperforms the compared solvers.