Absolute Values (a non-urgent but roundabout question)

I have a question which is apparently worth 4 marks (of 10!) which states that there is a possible 4 answers for the following:

Solve to which I simply worked out by expanding the LHS to and thus

I have no idea what other way I can look at this, so what am I missing?

If then .

But we have to choose the positive root, so

If then which has no real roots because the discriminant is negative.