How do you find the eigenvalue of A when you have the trace and determinant

Suppose that the trace of a 2x2 matrix A is tr(A)=7 , and the determinant is det(A)=6 . Find the eigenvalues of A.

How do I start doing this? can someone help me?

Let x and y be the two eigenvalues for A.
Then, det A = xy = 6
and tr A = x + y = 7.

Since y = 6/x, we obtain
x + 6/x = 7
==> x^2 - 7x + 6 = 0
==> (x - 6)(x - 1) = 0
==> x = 6 or 1.
==> y = 1 or 6, respectively.

Hence, the eigenvalues are 1 and 6.

I hope this helps!