In this note, following suggestions by Tao, we extend the randomized algorithm for linear equations over prime fields by Raghavendra to a randomized algorithm for linear equations over the reals. We also show that the algorithm can be parallelized to solve a system of linear equations $A x = b$ with a regular $n \times n$ matrix $A$ in time $O(n^2)$, with probability one. Note that we do not assume that $A$ is symmetric.