Identify the conic with equation x^2+3xy+4y^2-7=0, and find its center/vertex and axis.

My A matrix is (1 3/2; 3/2 4), which gives eigenvalues 1/2(5+3sqrt(2)) and 1/2(5-3sqrt(2))....these don't seem right as in every other problem, it comes out much nicer. Am I doing something wrong?