Solving the equation $11x^2-6000x-27500 =0$, preferably without the quadratic formula I obtained this form while solving an aptitude question.
$$\frac{3000}{x-50} + \frac{3000}{x+50} = 11$$
I changed it into quadratic equation
$$11x^2 -6000x - 27500 =0$$
but I don't know how to solve it.
I can't find two factor for 303500 that sums to 6000 or when I use formula the numbers become huge...
Without using calculator
how to solve it? is there any other simple way to solve [other method]? [or finding factor] I'm a beginner in math. Please explain your answer for me.

Hint
Do a substitution $x = 50y$. Then the equation becomes
$$
\frac {3000}{50(y-1)} + \frac {3000}{50(y+1)} = 11 \\
\frac {60}{y-1} + \frac {60}{y+1} = 11
$$
which should be a bit easier to solve... I guess...
