A lattice L is a discrete additive subgroup of some Euclidean space V. The lattice L is called well-rounded (WR) if its shortest vectors generate V. The image of an ideal I of a number field under embeddings is a lattice, we call it the lattice associated to I. The ideal I is called WR if the lattice associated to it is WR. Principal well-rounded (PWR) ideals relate to the shortest vector problem, sphere packing problem, and kissing number for ideals of number fields, as well as provide a variety of practical applications in coding theory. In this talk, we will show necessary and sufficient conditions for a real quadratic field to have PWR ideals. One of these conditions is a special Pell equation. Thus, finding these WR ideals requires solving Pell equations. Investigating the solutions of Pell equations, we can prove that there exist infinitely many real quadratic fields that have PWR ideals. Additionally, we construct algorithms to produce infinitely many non-similar PWR ideals.