Question 176937
Solve {{{sqrt(3x+1)}}} = {{{7 - sqrt(x-4)}}}
square both sides, you have to foil the right side
 3x + 1 = 49 - {{{14sqrt(x-4)}}} + (x-4)
:
 3x + 1 = 49 - {{{14sqrt(x-4)}}} + x - 4
:
 3x + 1 = x + 45 - {{{14sqrt(x-4)}}}
;
 3x - x  + 1 - 45 = {{{14sqrt(x-4)}}}
:
2x - 44 =  - {{{14sqrt(x-4)}}}
square both sides, FOIL the left side, remove the radical on the right
4x^2 - 176x + 1936 = 196(x-4)
;
4x^2 - 176x + 1936 = 196x - 784
:
4x^2 - 176x -196x + 1936 + 784 = 0
:
4x^2 - 372x + 2720 = 0 
Simplify divide by 4
x^2 - 93x + 680 = 0
Factors to
(x-8)(x-85) = 0
two solutions
x = 8
x = 85
:
Check both solutions in the original equation, only one is valid