One way to think about this is as distance. Since distance is always posative this will not have a solution.
Thank You Captain Obvious. Man, I'm losing it. Yeah, so what he's saying is that some equations can't be solved. The first time I ever came across equations with no solutions was with systems. I never seen anything like this. That's why I was thrown off. Think about it. How absurd is it to say that the absolute value of something is negative. Hello?!