Multiply both sides of equation by sqrt (4x-3) to get
4x + 7 = 7 sqrt(4x-3) square both sides
16x^2 + 56x + 49 = 196x-147 simplify
16x^2 -140x + 196=0 Simplify a bit by dividing by 4
4x^2 - 35x + 49=0
Use quadratic formula to find x = 7/4 and 7