2021 AMC 10A Problem 15

Values for A,B,C, and D are to be selected from \{1, 2, 3, 4, 5, 6\} without replacement (i.e. no two letters have the same value). How many ways are there to make such choices so that the two curves y=Ax^2+B and y=Cx^2+D intersect? (The order in which the curves are listed does not matter; for example, the choices A=3, B=2, C=4, D=1 is considered the same as the choices A=4, B=1, C=3, D=2.)

\textbf{(A) }30 \qquad \textbf{(B) }60 \qquad \textbf{(C) }90 \qquad \textbf{(D) }180 \qquad \textbf{(E) }360

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.