Fast Numerical Approximation to system of non-linear equations

I am currently looking into Halley’s Method. However, I wanted to see if there were better methods to solve the problem I am looking to solve.

Fast means a low number of iterations in my case. Also, due to the limitations of my processor, I would need to simplify the equations to additions, multiplications, divisions, and powers (also roots).

All capitalize letters are constants.

$XJ^2 = 2Vwidehat AJ + widehat A^3 + widehat D^3$

$widehat D^2 = VJ + widehat A^2$

$y^2 = VJ + A^2 + AJx$

$X = frac{2VAJ + A^3}{J^2} + frac{3A^2 + 2VJ}{2J}x + frac{A}{2}x^2 + frac{2VJ + 2A^2}{J^2}y + frac{2A}{j}xy – frac{1}{J^2}y^3$

I am trying to solve for $x$ or $y$, where $x > 0$ and x is in REALS. $widehat D neq D$ and $widehat A neq A$.

I have tried the substitution method and the aid of WolframAlpha to solve for the solution. The solution is often time are way too long or Wolfram does not recognize my query.

Again, I am looking for a fast numerical method to solve my problem (mainly the last 2 equations) — solve for x or y.The approximation threshold for $x$ is about 1E-11 based on empirical calculations.