Originally Posted by
Siron First of all, like SammyS said it has to be -2x in the numerator of the RS, because if it's 2x then you'll get a negative discriminant and so no roots in $\displaystyle \mathbb{R}$.
Rational inequality
$\displaystyle \frac{-2x-10}{x}>x+5$ and $\displaystyle x\neq 0$
Solve:
$\displaystyle \frac{-2x-10}{x}>x+5 \Leftrightarrow -2x-10>x(x+5) \Leftrightarrow -2x-10>x^2+5x \Leftrightarrow -x^2-7x-10>0 \Leftrightarrow -(x+5)(x+2)>0$
Now you can make a sign table to determine the solution.