It might looks simple, but it's a real challenge. In fact, if
, then f has 2 zeros. It means that the solution is not singular. But to prove it... not easy.
. We want to study its sign. So we want to find when it is equal to
.
.
Now if
. It means that
is decreasing from negative infinite to
. As when
,
,
is increasing from
to positive infinite.
f(0)=-4. As it will increase (strictly), it must cross the x axis on a single point when
. You can find a similar conclusion calculating for example
. It means that the roots of f are respectively between
and
. (5 because
). Now to find the roots, you can say that there is an easy one to see, when
. To calculate the other root, I suggest you the bisection method which will work.