Algebra

First, let's note that if there are no real solutions, then that means the descriminant is less than 0, 

Simplifying the quadratic equation a bit, we find that

$-15x^2-kx+53=0$

Since the descriminant is b^2-4ac, we have the equation

$k^2+3180<0$

This yields $k^2<-3180$

Note that this isn't possible. k^2 must be greater or equal to 0, so it cannot be equal to -3180. 

I might have done something wrong...not sure, but I think it's impossible

Thanks! :)