If I have a quadratic $Ax^2 + Bx + C$ where the coefficients contain an additional unknown $u$ for
$Ax^2+(bu+c)x+(du^2+eu+g)$
where $A$, $b$, $c$, $d$, $e$, $g$ are known
Is there a way to find solutions for $x$ and $u$ that satisfies
$0 = Ax^2+(bu+c)x+(du^2+eu+g)$