Algebra

For there to be no real solutions, the discriminant needs to be NEGATIVE

The descriminant is $b^2 - 4ac <0$  with  $b = k ;   \space a = 5   ; \space c = 8$

Plugging it all in, we have

$k^2 - 4(5)(8) <0 \\ k^2 < 160$

$k <   12.65$      

We are trying to find the largest INTEGER, which would be 12. 

Thanks! :)