Question: How do I solve second order equations and obtain real expressions?

I have been studying the solutions of the equation below using Maple and Mathematica. 

Here, I want to express the solutions for k. In Maple, the solution is imaginary. As one may see below.

On the other hand, if one solves that  exact equation with Mathematica, then one has real solutions. That is,

Based on the above, I have a few questions:

1. What is the correct solution for the first equation above? That is, are the solutions real or complex?

2. How may I obtain the real solutions, k_{1,2}, above using Maple?

Attached below you may find my mwfile with my doubts.

Thanks in advance.

Please Wait...