Inequality

x^3 + 4x > 5x^2 + 28x + x^3      simplify

5x^2 + 24x  <  0 

x ( 5x + 24)  <  0

Setting the equation equal to 0  and  solving for  x produces   x =  -24/5  and x =  0

The solution comes from either (-inf, -24.5)  or (-24.5, 0) or ( 0 ,inf)

Testing a point in each interval :

The solution comes from      ( -24.5 , 0)