Question 178168
Solve √(2x+3) - √(2x)=1

Square both sides to get:

2x+3 -2sqrt(2x(2x+3) - 2x = 1

Combine:
-2sqrt(4x^2+6x) = -2

sqrt(4x^2+6x) = 1
Square both sides to get:

4x^2 + 6x = 1

Rearrange:
4x^2 + 6x -1 = 0
Use quadratic formula:

x = [-6 +- sqrt(36 - 4*4*-1] / 8

x = [-6 +- sqrt(52)/8

x = [-6 +- 2sqrt(13)]/8

x = [3 +- sqrt(13)]/4
============================
Check the answers to see if any are extraneous.
===============================================
Cheers,
Stan H.