This paper considers signal detection in massive multiple-input multiple-output (MIMO) systems with general additive hardware impairments and one-bit quantization. First, we present the quantization-unaware and Bussgang decomposition-based linear receivers by generalizing them for the considered hardware impairment model. We propose an optimization problem to estimate the uplink data signals by choosing a suitable cost function that treats the unquantized received signal at the base station as the variable. We exploit the additional structure of the one-bit quantization and signal modulation by including proper constraints. To solve the non-convex quadratically-constrained quadratic programming (QCQP) problem, we propose an ADMM-based algorithm with closed-form update equations. Then, we replace the harsh projectors in the updates with their soft versions to improve the detection performance. We show that the proposed ADMM-based algorithm outperforms the state-of-the-art linear receivers significantly in terms of bit error rate (BER) and the performance gain increases with the number of antennas and users.