Function with 2 unknowns and one needs to be solved I have a homework question stating:

Find the set of values of $k$ for which $f(x)=3x^2-5x-k>1$ for all $x\in\mathbb R$.

This question has really confused me because I looked at the answer and the value of $k$ is meant to be $k<-\frac{37}{12}$ and I'm afraid I don't know how to get there. May I please have some help?

Hint
Consider the function
$$f(x)=3x^2-5x-k-1$$
Its derivative $f'(x)=6x-5$ is zero when $x=\frac 56$ and you want that $f\left(\frac{5}{6}\right) >0$.
Then, ....
