help need help

First, let's simplify this equation. Combining all like terms, we have

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

Now, in order for the value of x to not be real, then the descriminant must be negative. 

Thus, we have

${\left(-k\right)^2-4\left(-15\right)\cdot \:53} < 0$

Now, we simplfy solve for k. We get that

$k^{2}-3180 < 0\\ k^2 < 3180\\ -2\sqrt{795} <2\sqrt{795}\\ -56.39 < k < 56.39$

The largest integer k can be that fits in the range given for k is 56. 

So our answer is just 56. 

Thanks! :)