If g left parenthesis x right parenthesis equals 36 x squared minus 36 and h left parenthesis x right parenthesis equals 65 x, then solve g left parenthesis x right parenthesis greater than h left parenthesis x right parenthesis .

Given
g(x) = 36x² -36
h(x) = 65x

Find
x such that g(x) > h(x)

Solution
We can start by substituting the given information into the required relation.
  36x² -36 > 65x
Subtracting the right side and factoring gives
  36x² -65x -36 > 0
  (9x +4)(4x -9) > 0

The product of these factors will be greater than zero when both factors are negative or both are positive. They change sign at x = -4/9 and x = 9/4. Hence, the solution is
  x < -4/9 or 9/4 < x