Solving quadratic equations with radicals on a computer with floating-point arithmetic requires great care to handle correctly all possible parameters. Literature on the subject glosses over the details, often considered as important but tedious to present. As a consequence, most implementations are flawed in one way or another. After having reviewed both the literature and the actual implementations in several programming languages and applications, we present an algorithm inspired from an exposition by Pat Sterbenz from 1974, adapted to take advantage of more recent researches in the field, which leads to a robust quadratic equation solver.