sqrt(7x+1) - sqrt(x-5) = 6
a + b = c
a^2 + 2ab + b^2 = c^2
(7x+1) +2 * sqrt(7x+1) * sqrt(x-5) + (x-5) = 36
2 * sqrt(7x+1) * sqrt(x-5) + 8x - 4= 36
2 * sqrt(7x+1) * sqrt(x-5) = -8x + 40
a * b * c = d
a^2 * b*2 * c^2 = d^2
4 * (7x+1) * (x-5) = (-8x + 40)^2
4 * (7x^2 + x - 35x -5) = (-8x + 40)^2
4 * (7x^2 - 34x - 5) = (-8x + 40)^2
28x^2 - 136x - 20 = (-8x + 40)^2
28x^2 - 136x - 20 = 64x^2 - 640x + 1600
-36x^2 - 136x - 20 = -640x + 1600
-36x^2 + 504x - 20 = 1600
-36x^2 - 504x - 1620 = 0
4x^2 + 56x + 180 = 0
x^2 + 14x + 45 = 0
(x+5) (x+9) = 0
x = -9, -5