Observing that \(x^2-5x=x(x-5)\) tells us that the roots are:\(\displaystyle x^2-5x>0 \) becomes \(\displaystyle x(x-5)>0\) or \(\displaystyle x^2>5x\) depending on what I do. I'm just not sure where to take it after that.
So, since the coefficient of the squared root is positive, I can tell it's \(\displaystyle (\infty,0)\cup(5,\infty)\)?Observing that \(x^2-5x=x(x-5)\) tells us that the roots are:
Rather than testing intervals though, let's use what we know about the parabolic graphs of quadratic functions. We see the coefficient of the squared term is positive, which means the parabola opens upwards, and so, given that it has two real roots, we should expect the expression to be positive on either side of the two roots, and negative in between. Can you proceed?