Question 1206414
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I appreciate you showing your work. 
The jump from 
(-2x+2)/2=2(sqrt(3x-3))/2
to 
(-x)^2=(sqrt(3x-3))^2
is incorrect. See lines 6 and 7.


The (-2x+2)/2 should turn into -x+1
The 2s cancel on the right hand side.


This is what you should have for line 7
-x+1 = sqrt(3x-3)


Afterward you would square both sides to get
(-x+1)^2 = 3x-3
I'll let you finish up. 
Keep in mind that you'll need to check each possible solution in the original equation to ensure it's an actual solution. 
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