hi, i've got the question-

find the range of values of the constant c for which the line $\displaystyle y = 3x + c$ does not intersect the parabola with equation $\displaystyle y = 2x^2 + 5x - 7$

i know you have to have a discriminant thats less than 0 for this so i strted by putting the equation into one like this $\displaystyle 2x^2 + 2x + (-7 - c)$ so then used the theory : $\displaystyle (2)^2 - 4(2)(-7-c)$ which came to $\displaystyle 4 - (- 56 - 8c)$ which then became $\displaystyle (60 - 8c) < 0$ then i made it $\displaystyle - 8c < - 60$ leaving $\displaystyle c < 7.5$.

the answer the book gives me is $\displaystyle c < - 7.5$

can some explain this please? thanks