2sqrt(3x+7) -2=x+3

2√(3x + 7) - 2  =  x + 3

Add 2 to both sides:

2√(3x + 7)  =  x + 5

Divide both sides by 2:

√(3x + 7)  =  (x + 5)/2

Square both sides:

3x + 7  =  (x² + 10x + 25)/4

Multiply both sides by 4:

12x + 28  =  x² + 10x + 25 

Subtract 12x + 28 from both sides:

0  =  x² - 2x - 3

Factor:

0  =  (x - 3)(x + 1)

Solve:

x = 3     or     x = -1