First, we need to isolate the square root on the left-hand side of the equation. We can do this by squaring both sides of the equation. This gives us:
9x^2-4x+4=(2(3x-2)+sqrt(x))^2
Expanding the right-hand side of the equation gives us:
9x^2-4x+4=12x^2-12x+4
Subtracting 12x^2-12x+4 from both sides of the equation gives us:
-3x^2+8x-0=0
Factoring the left-hand side of the equation gives us:
-(x-2)(3x-0)=0
This gives us two possible solutions for x:
x=2 x=0
However, the value of x=0 is not a valid solution, because it would make the square root on the left-hand side of the original equation undefined. Therefore, the only valid solution is x=2.
