I would like to use Hensel's Lemma to lift the solution to the following equation: $$f(x,y,z)=5x^2+7y^2-13z^2$$ in $Q_2$. The way I tried to approcah this problem is to find such $x_0,y_0,z$ so that $x_0, y_0$ are fixed and $f(z)\equiv 0\pmod p$ and $f'(z)\not\equiv 0\pmod p$ and then apply Hensel's Lemma. But I was not able to find any such $x_0,y_0,z$.
Thank you!