To rearrange the equation d = vit + 1/2 at^2 for time (t), the solution involves using the quadratic formula. The derived formula is t = (-Vi ± √(Vi² + 2ad)) / a, where Vi is the initial velocity, a is acceleration, and d is distance. The discussion highlights that while this formula is valid, it may be more practical to use alternative equations for solving motion problems. The complexity of the derived formula can make it less appealing for quick calculations. Ultimately, understanding the context and choosing the simplest method is key in physics problem-solving.