Find the range of values of $\displaystyle k$ if $\displaystyle kx^2 + 8x > 6 - k$ for all real values of $\displaystyle x$.
The answer given is k > 8.
Find its discriminant and solve the equation discriminant=0 for k; then take a value of k which (i) is smaller than the smaller root, (ii) is higher than the higher root and (iii) lies between the two roots. Take that region which satisfies the equation you mentioned.