I was solving a math question on an online test, and the question was asking what is possible values of $x$ if the perimeter of some rectangle tile is between $20$ cm and $54$ cm. I wondered how we would find possible values of $x$ if the area was between $20$ and $54$ cm.
I thought we could use sign analysis for each inequality, but I understood that won't work because we will be having different inequalities in each part and that doesn't make sense.
Inequality looks like this: $20<2x^2+12x<54$
How could we solve quadratic inequalities with two boundaries like this?