How do i find x in this function?

√(3x + 4) - 2x  =  2

To get rid of a square root, you will need to square both sides. However, before you do that, get the square root term alone on one side.

Add 2x to both sides:

√(3x + 4)  =  2x + 2

Now square both sides:

( √(3x + 4) )²  =  ( 2x + 2 )² 

       3x + 4  =  4x²  + 8x + 4

Getting all the terms to one side:

     4x²  + 5x  =  0

Factoring:

     x(4x + 5)  = 0

--->     Either  x  =  0     or     4x + 5  = 0

So, either  x = 0  or  x = -5/4.

Checking in the original problem:  x = 0  --->   √(3(0) + 4) - 2(0)  =  √(4)  =  2    Correct!

x = -5/5   --->   √(3(-5/4) + 4) - 2(-5/4)  =  √(1/4) + 10/4   1/2 + 5/2  =  6/2  =  3     Not correct!

So, the only answer is:  x = 0.