Algebra

First, let's simplify and combine all like terms. 

After doing that, we get $3x^2-kx+33=0$

Now, in order for the equation to have no real solutions, the descriminant must be less than 0. 

The descriminant is $b^2-4ac$, so we have the equation $k^2 - 4(33)(3) < 0$

Since we are trying to find the largest, we set the two to equal each other and get

$k^2 - 396 = 0\\ k^2 = 396\\ k \approx 19.89974$

Rounding down, the largest k can be as an integer is 19. 

So our answer is 19. 

Thanks! :)