On the distribution of the roots of a quadratic congruence

The author obtains the following estimate
$$ \sum_{d\leqslant x}\,\sum_{\begin{subarray}{c}{0<f\leqslant d}\\{f^2+2rf-\beta\equiv0 \pmod{d}}\end{subarray}}\left(\frac fd\right)\ll x^{\frac58+\varepsilon}, $$
where $\left(\frac fd\right)$ is the Kronecker symbol and $\beta\ne\Box$, $r^2+\beta\ne\Box$.