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! :)