Question 194802
1)  sqrt (x) -5 =7
,,,,sqrt(x) =12
squaring
x = 144
checking
sqrt(144) -5  =12-5 =7,,,,ok
or  if  the  problem  is  
sqrt (x-5) =7
squaring 
x-5 =49
x=54
checking
sqrt(54-5) = sqrt(49) =7,,,ok
.
2)  sqrt (3x) / sqrt(2x+3) =2
squaring
(3x)  /  (2x+3)   =  4
cross  multiply
3x = 4 (2x+3) = 8x +12
-5x = 12
x=(-12/5)  ,,,,,,ANSWER
checking
sqrt(3(-12/5) / sqrt( 2(-12/5) +3)  =  2
sqrt  -36/5 / sqrt (-24 /5 +3)  =2
sqrt -36/5 / sqrt ( -24/5 +15/5) =2
sqrt -36 /5 / sqrt -9/5  =2
sqrt ( -36 /-9) = sqrt (4) =2
2=2,,,,,,ok
.
3)  sqrt(x+5) = x+3
squaring
(x+5) = (x+3)^2 = (x+3)(x+3) =x^2 +6x +9
0 = x^2  +5x  +4
0 = ( x+1) (x+4)
x = -1,  -4
checking
x=-1  ,,,, sqrt(-1+5) = (-1+3),,,,sqrt 4 = 2,,,,,,,ok
for  x=-4,,,,,,sqrt ( -4+5)  = (-4+3),,,sqrt (1) = -1,,, ok,,,realizing  sqrt1= +/- 1