sqrt(-v+27)=v+3

√(-v + 27)  =  v + 3

To get rid of a square root, square both sides:

  -v + 27  =  (v + 3)²                         (v + 3)²   =  (v + 3)(v + 3)  =  v²  + 3v + 3v + 9  =  v²  + 6v + 9

  -v + 27  =  v²  + 6v + 9

Since it is a quadratic, get all terms to one side; add v to both sides and subtract 27 from both sides.

  0  =  v²  + 7v - 18

  0  =  (v + 9)(v - 2)

So, either v = -9 or v = 2.

Checking answers, 2 works but -9 doesn't.