When you take away the absolute value, you have 2 possible solutions. One positive version on the other side and one negative. In this case, they give the same result. So will just need to do one version.
To get rid of the square root, square both sides.
(4x-3)(4x-3)=52(√x+4)2 Simplify using FOIL, squaring 5 and removing the radical symbol when you square it.
16x2-24x+9=25(x+4) Distributive property
16x2-24x+9=25x+100 Subtract 25x and 100 from both sides
16x2-49x-91 = 0 Solve using the quadratic formula
a=16, b=-49 and c=-91
x=-1.3029 and 4.3654