sqrt(x) + sqrt(3x+4) = sqrt(6x+12)
a + b = c
(a + b)^2 = c^2
a^2 + 2ab + b^2 = c^2
x + 2 * sqrt(x) * sqrt(3x+4) + 3x + 4 = 6x + 12
2 * sqrt(x) * sqrt(3x+4) + 4x + 4 = 6x + 12
2 * sqrt(x) * sqrt(3x+4) = 2x + 8
a * b * c = d
a^2 * b^2 * c^2 = d^2
4 * x * (3x+4) = (2x+8)^2
12x^2 + 16x = (2x+8)^2
12x^2 + 16x = 4x^2 +32x + 64
8x^2 + 16x = 32x + 64
8x^2 - 16x = 64
8x^2 - 16x - 64 = 0
8 (x^2 - 2x - 8) = 0
8 (x-4) (x+2) = 0
x = -2, 4