# Is there integer $x$ such that $79|7x^2+4x-23$

Is there integer $$x$$ such that $$79|7x^2+4x-23$$ ?

I keep getting that there is $$x$$ that satisfies this condition, but online calculator keeps saying that there is not. I worked it out using Legendre's symbol:

If $$y=7x+2$$, then starting equation is equivalent to $$y^2 \equiv 7$$ mod$$79$$, and because $$\genfrac{(}{)}{}{}{7}{79} = \genfrac{(}{)}{}{}{79}{7} = 1$$, equation has a solution ?

Note that by quadratic reciprocity $$\left(\frac{7}{79}\right)=(-1)^{3\cdot39}\left(\frac{79}{7}\right)=-\left(\frac{2}{7}\right)=-1.$$