Solve the equation $\sqrt{3x-2} +2-x=0$ 
Solve the equation: $$\sqrt{3x-2} +2-x=0$$

I squared both equations $$(\sqrt{3x-2})^2  (+2-x)^2= 0$$ 
I got $$3x-2 + 4 -4x + x^2$$
I then combined like terms $x^2 -1x +2$
However, that can not be right since I get a negative radicand when I use the quadratic equation. 
$x = 1/2  \pm \sqrt{((-1)/2)^2 -2}$
The answer is 6

If you meant
$$\sqrt{3x-2}+2-x=0\implies \sqrt{3x-2}=x-2\implies3x-2=(x-2)^2=x^2-4x+4\implies$$
$$\implies x^2-7x+6=0$$
Now just check that $x^2-7x+6=(x-6)(x-1)$ ...and remember to check at the end whether both solutions of this quadratic are actually solutions of your original equation, since when squaring some mess can happen there. For example, one of the soltuions of the quadratic is not a solution of your equation.
