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Before running off it it smart to take a look at two things:
1. The number under the radical, 6x+2
2. The result of the square root, x-1
If you think about it, both numbers must be >=0!
6x+2 >=0 because there is no (real) square root of a negative number.
x+1 >=0 because it's a square root and that is >=0 by definition.
This means that you answers are restricted two ways:
1. 6x+2>=0, so 6x>=-2, x>=2/6, x>=1/3
2. x-1>=0, so x>=1
BOTH must hold, so we combine them: x>=1.
Whatever "solutions" you may find, they MUST be >= 1.
Now square everything in sight:
(x-1)² = 6x+2
Work out the brackets
Everything to the left side of the =-sign
Factorize, or use abc-formula
Check the solutions! Only if they are >= 1 they are really solutions.
Reason for this nitpicking: by squaring everything, you lose the information about the square root and you could get fake solutions...
Oops, typo: 6x>=-2, so x>= -1/3
Makes no difference: x >=1 anyway.
@nubeer: I wouldn't *start* with squaring, see above reasoning...