Two poles $A B$ of length $a$ metres and $C D$ of length $a + b ( b \neq a )$ metres are erected at the same horizontal level with bases at $B$ and $D$. If $B D = x$ and $\tan \angle A C B = \frac { 1 } { 2 }$, then:
(1) $x ^ { 2 } + 2 ( a + 2 b ) x - b ( a + b ) = 0$
(2) $x ^ { 2 } + 2 ( a + 2 b ) x + a ( a + b ) = 0$
(3) $x ^ { 2 } - 2 a x + b ( a + b ) = 0$
(4) $x ^ { 2 } - 2 a x + a ( a + b ) = 0$