In:
Det[{{7 - z, k}, {-9, 5 - z}}]
Discriminant[%, z]
Solve[% == 0]
Out:
35 + 9 k - 12 z + z^2
-4 (-1 + 9 k)
{{k -> 1/9}}
In:
Det[{{7 - z, k}, {-9, 5 - z}}]
Discriminant[%, z]
Solve[% == 0]
Out:
35 + 9 k - 12 z + z^2
-4 (-1 + 9 k)
{{k -> 1/9}}