Parabola/Analytic Geometry - $y=kx+5$ intersects for all values of $k$ with parabola $y=x^2+2$

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The question states:

Show that the line $y=kx+5$ intersects with the Parabola $y=kx+2$ for all values of k.

I thought this would be similar to the other problems where I use the discriminant but the answer ends up not being real... ?

I set them equal to each other,

$x^2+2=kx+5$

$x^2-kx-3=0$

$Δ=κ^2-4(-3)(1)$

Then I set this to 0 to find intersection, but it doesn't have a real intersection.

$k^2+12=0$

Any ideas?