Solving Algebraic Fractions

I'm having to solve some algebraic fractions, which is like normal algebra, but with fractions involved basically. I've got this:

$\displaystyle

\frac{1}{x+1}+\frac{1}{x-1}=4

$

And through algebra, I've got to this (if you want to post the entire process of how I got to it, then please ask):

$\displaystyle

2x^2-x-2=0

$

And I can't factorise this and solve it, nor does it work if I plug it into the quadratic formula, because I end up trying to square root a minus number (again, ask if you want to know how I got to it):

$\displaystyle

x=\frac{1\pm\sqrt{-63}}{8}

$

Now, I wouldn't mind ending up with an in-solvable quadratic, but the question specifically states to SOLVE the equation, so I'm kind of stuck now. I've been over it several times, and given it to my Dad to have a try, and he got to the same stage that I did, and I'm pretty sure I haven't made a mistake (of course, it could just be a silly mistake that we both somehow made, but I think the chance of this is pretty low).

I could wait to ask my teacher, but the point of this homework is to practice solving these, and to learn from mistakes I make, so if someone could see what the problem is, then could you help me?