SOLUTION: the squareroot of -12 + 2x = the squareroot of 3x+23 please provide step by step

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Question 265331: the squareroot of -12 + 2x = the squareroot of 3x+23
please provide step by step
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
the squareroot of -12 + 2x = the squareroot of 3x+23
(2x-12)^1/2 = (3x+23)^1/2
Take the square on both sides of the equation
2x-12=3x+23
2x-3x=23+12
-x=35
x=-35

Answer by ikleyn(53742) About Me  (Show Source):
You can put this solution on YOUR website!
.
the squareroot of -12 + 2x = the squareroot of 3x+23
please provide step by step
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        The solution in the post by @mananth is fatally wrong.
        See my correct solution below. 


Our starting equation is

    sqrt%282x-12%29 = sqrt%283x%2B23%29.


Take the square on both sides of the equation

    2x - 12  = 3x + 23

    -12 - 23 = 3x - 2x

       x    =    -35


But x = -35 makes the expression  2x-12  negative under the square root in the left side of the original equation.


So, we conclude that given equation has no real solution.

Solved correctly.