Solve for x: 1/(x+1) + 2/(x+2) = 4/(x+4), x ≠ -1, -2, -4

By cross multiplying, we get
(x+2) + 2(x+2)/(x+1) = 4(x+1)/(x+4)
(x+2+2x+4)(x+4) = 4(x+1)(x+2)
(3x+6)(x+4) = 4(x^2+3x+2)
3x^2+12x+4x+24 = 4x^2+12x+8
x^2 - 4x -16 = 0
We have a formula for solving quadratic equation ax^2+bx+c=0 which is
x = (-b ± √(b^2 - 4ac))/2a
x = (4 ± √(16 + 64))/2
x = (4 ± √80)/2
x = (4 ± 4√5)/2
x = 2 ± 2√5
x = 2 + 2√5, 2 - 2√5