### Solving a polynomial system in a quotient ring

I want to compute all solutions ~~over $\mathbb{Z}_9$ ~~in ~~parameters $a,b,c$ ~~$\mathbb{Z}_9[\sqrt2,x]$, where $x$ is such that $(x+\sqrt2)^2=2(x+\sqrt2)$, of the equation

~~$$(ax+b\sqrt2+c)^2=1$$~~

where $x$ is such that $(x+\sqrt2)^2=2(x+\sqrt2)$.$$X^2=1.$$

I'm first defining the polynomial ring over $\mathbb{Z}_9$ in variables ~~$a,b,c,x,y$, ~~$x,y$, then factoring by the ideal generated by

$$y^2-2, (x+y)^2-2(x+y),$$

but then I don't know which command to use in order to get the ~~solutions. ~~solutions of $X^2-1$. I have tried "solve" and "variety", but they do not seem to work. The code up to this point is just

~~R.<x,y,a,b,c> ~~R.<x,y> = PolynomialRing(IntegerModRing(9),order='lex')
J= R.ideal(x^2-2,(x+y)^2-2*(x+y))
S=R.quotient(J)

Which function should I use?