This paper studies the problem of detection of dental diseases. Dental problems affect the vast majority of the world's population. Caries, RCT (Root Canal Treatment), Abscess, Bone Loss, and missing teeth are some of the most common dental conditions that affect people of all ages all over the world. Delayed or incorrect diagnosis may result in mistreatment, affecting not only an individual's oral health but also his or her overall health, thereby making it an important research area in medicine and engineering. We propose a pipelined Deep Neural Network (DNN) approach to detect healthy and non-healthy periapical dental X-ray images. Even a minor enhancement or improvement in existing techniques can go a long way in providing significant health benefits in the medical field. This paper has made a successful attempt to contribute a different type of pipelined approach using AlexNet in this regard. The approach is trained on a large dataset of 16,000 dental X-ray images, correctly identifying healthy and non-healthy X-ray images. We use an optimized Convolutional Neural Networks and three state-of-the-art DNN models, namely Res-Net-18, ResNet-34, and AlexNet for disease classification. In our study, the AlexNet model outperforms the other models with an accuracy of 0.852. The precision, recall and F1 scores of AlexNet also surpass the other models with a score of 0.850 across all metrics. The area under ROC curve also signifies that both the false-positive rate and false-negative rate are low. We conclude that even with a big data set and raw X-ray pictures, the AlexNet model generalizes effectively to previously unseen data and can aid in the diagnosis of a variety of dental diseases.