20/x^+4x=3/x+4+1/x
2(2x+3)/2x=x(x+5)/2x
4x+6 =x^+5x
x^+5x-4x-6
x^+x-6
(x+1)(x-6)
Is your first line,
20/(x^2 + 4x) = 3/(x+4) + 1/x ??
I will assume that, then
20/(x(x+4)) = 3(x+4) + 1/x
your LCD is x(x+4) , so let's multiply each term by that ...
20 = 3x + x+4
16 = 4x
x = 16/4 = 4
The rest of your post has no relation to your first equation.
If it is a new equation, then
4x+6 = x^2 + 5x is correct, but then
x^2 + x - 6 = 0
(x+3)(x-2) = 0
x = -3 or x = 2