Implicit Differentiation: Find $\frac{d^2y}{dx^2}$ Find $\frac{d^2y}{dx^2}$ of:

$$4y^2+2=3x^2$$

My Attempt
I attempted the probelm my first solving for the first derivative:

$8y*y'=6x$
$y'=\frac{3x}{4y}$

Then I tried it again; however I was a bit confused, and ended up getting

$y''=\frac{6y-3x(2*y')}{16y^2}$

Would I substitute in the first derivative back in to get:

$y''=\frac{6y-6x(\frac{3x}{4y})}{4y^2}$

and then finally
Final Answer
$$y''=\frac{6y^2-9x^2}{4y^3}$$
Is my final answer correct, if not what is the correct answer please?

For future reference,
$F(x,y)=0$
$\frac{d^2[F(x,y)]}{dx^2}=-\frac
{\frac{\partial^2 F}{\partial x^2}\left(\frac{\partial F}{\partial y}\right)^2
-2·\frac{\partial^2 F}{\partial x\partial y}·\frac{\partial F}{\partial y}·\frac{\partial F}{\partial x}
+\frac{\partial^2 F}{\partial y^2}\left(\frac{\partial F}{\partial x}\right)^2}
{\left(\frac{\partial F}{\partial y}\right)^3}$
