Let \(b,c\) be integers with \(\Delta=b-4c\) not a square, and let \(d(n)\) denote the number of positive divisors of a non-zero integer \(n\). In [J. McKee, Math. Proc. Camb. Philos. Soc. 117, 389-392 (1995; Zbl 0841.11050)], the author obtained an explicit expression for the constant \(\lambda\) in the formula \[ \sum_{n\geq x}d(n^2+bn+c) =\lambda X\log X+O(X) \] for the case \(\Delta<0\); the value of \(\lambda\) is given in terms of the Kronecker/Hurwitz class number \(H^*(\Delta)\). In this paper, the more difficult problem of determining \(\lambda\) when \(\Delta>0\) is tackled. Here the automorphism groups corresponding to those used to define \(H^*(\Delta)\) when \(\Delta<0\) are infinite. The key idea employed to overcome this is to utilize the index of a certain subgroup of the automorphism group in the definition of \(H^*(\Delta)\) instead of the cardinality of the automorphism group. When \(\Delta <0\), this definition reduces to the original definition except in the cases \(\Delta=-3\) or \(-4\).