What's the proper way of solving this inequality problem?

>The temperature T in °C at a distance of x meters near a campfire is given by the following formula: T= 600,000/ (x^2 +300). At which distance interval from the campfire would the temperature be lower than 500°C?

My first step would be to settle the Inequality as 600,000/ (x^2 +300)<500 and solve x from there. I could find the critical points by treating it as a common equation and the answer for x is +30 and -30, then assume farther 0 is colder.

However, the book says when solving inequalities you cant simply multiply denominators with variables in them because you don't know yet the values for which the denominator would be lower than zero, which would flip the inequality, instead we should substract from one side to make it zero and I get

> (450,000-500x^2)/(x^2+300)<0

However I can't find x by the zero product property for the denominator since when applying the quadratic formula it only has a complex solution.

How is this supposed to be solved using inequality properties then?