Stuck while Solving a Rational Equation

[needsmajorhelp]

so here is the original problem;
Solve. Use a solution set or interval notation where appropriate.

2x/(x-2) + 5/(x-4) = 13/(x^2+2x-8)

this is what i've gotten so far.

2x(x-4)(x+4)+5(x-2)(x+4)-13(x-4)=0
2x(x^2-16)+5(x^2+2x-8)-13x+52=0
2x^3-32x+5x^2+10x-40-13x+52=0
2x^3+5x^2-35x+12=0

and im stuck. i cant factor and i tried using quadratic formula with c=-35x+12
but got stuck figuring out how to check the answer. just wanted to know if i was doing it right.

this is the answer i ended up with:
[-5 +/- (-167+560x)^(1/2)]/4

please help, if you can. thanks!

[stapel_eliz]

2x^3+5x^2-35x+12=0

and im stuck. i cant factor and i tried using quadratic formula

Since this is not a quadratic (nor of any quadratic-type form), the Quadratic Formula does not apply. You'll need to use more advanced techniques for solving the polynomial equation, starting with the Rational Roots Test.

[needsmajorhelp]

thanks so much. my teacher used x+5 as equal to c in a quad form once.
but she sent out an email saying that she meant 5/x+4 as the original problem!
phew that makes it easier!
thanks for your help!