My equation is $\displaystyle x^2+2kx-5=0$

I have to find the discriminate for this assuming it has 2 real roots

so I do $\displaystyle b^2-4ac$ is greater than 0

$\displaystyle (2k)^2-4(-5)$ is greater than 0

$\displaystyle k^2$ is greater than -5

k= plus or minus square route of -5

I seem to have done the discriminate well but how can a complex number be the solution for the discriminate since I am supposed to have 2 real roots?

I also encountered the same problem trying to do $\displaystyle x^2+2kx-7=0$ (but with this time the square route of -7). Can anyone help out please? Thanks.