If you would like to know the value of k and the other solution, you can find this using the following steps:
z = 3
5z^2 + k z - 30 = 0
5 3^2 + k 3 - 30 = 0
5 9 + 3 k - 30 = 0
45 - 30 + 3 k = 0
3 k = - 15
k = - 15/3
k = - 5
5z^2 - 5z - 30 = 0 /5
z^2 - z - 6 = 0
(z - 3) (z + 2) = 0
z^2 + 2z - 3z - 6 = 0
1. z = 3
2. z = - 2
The correct result would be: k = - 5 and z = - 2.
