Solving $\frac{dy}{dx}=\sqrt{3x+2y}-\frac{3}{2}$ without stuff from higher-order differential equations

Question

I'm trying to solve this equation:
$$\frac{dy}{dx}=\sqrt{3x+2y}-\frac{3}{2}$$
without using stuff from higher-order differential equations.

I've tried using substitution $ w=\frac{y}{x} $, but it doesn't really help. After using that substitution, I get
$$ \frac{dw}{dx}=\frac{\sqrt{x}\sqrt{3+2w}-\frac{3}{2}w}{x} $$
which isn't a differential equation with separable variables.

Can somebody please help me out with this one?

Answer 1

Hint: Substitute $u = 3x + 2y$. It should then be separable.