Detecting and segmenting individual cells from microscopy images is critical to various life science applications. Traditional cell segmentation tools are often ill-suited for applications in brightfield microscopy due to poor contrast and intensity heterogeneity, and only a small subset are applicable to segment cells in a cluster. In this regard, we introduce a novel supervised technique for cell segmentation in a multi-task learning paradigm. A combination of a multi-task loss, based on the region and cell boundary detection, is employed for an improved prediction efficiency of the network. The learning problem is posed in a novel min-max framework which enables adaptive estimation of the hyper-parameters in an automatic fashion. The region and cell boundary predictions are combined via morphological operations and active contour model to segment individual cells. The proposed methodology is particularly suited to segment touching cells from brightfield microscopy images without manual interventions. Quantitatively, we observe an overall Dice score of 0.93 on the validation set, which is an improvement of over 15.9% on a recent unsupervised method, and outperforms the popular supervised U-net algorithm by at least $5.8\%$ on average.