بسم الله الرحمن الرحيم
(Fatwa: 796/786/N=08/1437)
(1) Had you sent the question by sending the talaq paper it would have been better.
However the answer to your question is that you have given talaq bain to your wife then talaq bain occurred on her without any doubt. The ruling pertaining to talaq bain is that you cannot take her back into your nikah. And she shall go completely out of your nikah after iddah. However if you have given her less than three talaqs, two or one talaq bain, then you may take her back by doing new nikah within iddah or after iddah with mutual consent. However in future, you shall have only the right of leftover talaq i.e. one or two talaqs.
إذا كان الطلاق بائناً دون الثلاث فله أن يتزوجها فى العدة وبعد انقضائها …. كذا فى الهداية (الفتاوى الهندية ، كتاب الطلاق، باب فى الرجعة ، فصل في ما تحل به المطلقة وما يتصل به 1:473، ط: مكتبة زكريا ديوبند)
Allah knows Best!
Darul Ifta,
Darul Uloom Deoband