Originally Posted by
emakarov $\displaystyle x^2 + 6x - 5 > 8x + k\iff x^2 - 2x - (5+k) > 0$. Do you know how to determine if a quadratic polynomial has no roots?
Another way is to sketch the graphs of f(x) and g(x) and to understand that the line that is the graph of g(x) with the critical value of k is a tangent to the parabola that is the graph of f(x). Find the slope of f(x) (it depends on x) and equate it to the slope of g(x) (which is constant). From this equation, find x and y = f(x) and then find k such that g(x) passes through (x, y).