In this case, since x represents the length of the diagonal of the trapezoid, it wouldn't be possible for x/2 to be a negative number. In general, though, you are right; this equation falls in to the category of "quadratic equations," which have an x-squared term. It's possible to show that quadratic equations always have two solutions.
You can see Prof. Loh talk about a cool way of solving quadratic equations which he came up with while developing Module 4: Algebra Tools. You can also read more about him and his quadratic method in this NYT article.
The Daily Challenge Team