The paper presents an explicit expression for the distribution of the positive definite quadratic forms in the normal case, this problem is the same as that of a weighted chi-square variates with positive weights. Two results are introduced, the first deals with the exact explicit form of the density function of the weighted chi-square variates with even degrees of freedom, and the second is a generalization to deal with the case of odd or/and even degrees of freedom. result of the later case which is an approximation in the case of odd values was shown to be mixture of two density functions of the first type. The distribution is shown to be a finite series of gamma functions.