Geodesic
On the distribution of the roots of a quadratic congruence
Zapiski Nauchnykh Seminarov POMI, Modular functions and quadratic forms. Part 1, Tome 183 (1990), pp. 155-165

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The author obtains the following estimate $$ \sum_{d\leqslant x}\,\sum_{\begin{subarray}{c}{0\leqslant d}\\{f^2+2rf-\beta\equiv0 \pmod{d}}\end{subarray}}\left(\frac fd\right)\ll x^{\frac58+\varepsilon}, $$ where $\left(\frac fd\right)$ is the Kronecker symbol and $\beta\ne\Box$, $r^2+\beta\ne\Box$. 
@article{ZNSL_1990_183_a7,
     author = {O. M. Fomenko},
     title = {On the distribution of the roots of a quadratic congruence},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {155--165},
     publisher = {mathdoc},
     volume = {183},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1990_183_a7/}
}
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O. M. Fomenko. On the distribution of the roots of a quadratic congruence. Zapiski Nauchnykh Seminarov POMI, Modular functions and quadratic forms. Part 1, Tome 183 (1990), pp. 155-165. http://geodesic.mathdoc.fr/item/ZNSL_1990_183_a7/