Factor $6x^2​ −7x−5=0$ I'm trying to factor
$$6x^2​ −7x−5=0$$
but I have no clue about how to do it. I would be able to factor this:
$$x^2-14x+40=0$$
$$a+b=-14$$
$$ab=40$$ 
But $6x^2​ −7x−5=0$ looks like it's not following the rules because of the coefficient of $x$. Any hints?

Here is a proof from Sierpinski, Waclaw: Elementary theory of numbers
Let us assume that $a_m,\ldots,a_0$ are integers and $x=\frac{k}{s}$ is a solution of
$$a_mx^m+a_{m-1}x^{m-1}+\cdots+a_1x+a_0=0 \tag{1}$$
with 
$$(k,s)=1 \tag{2}$$
then
$$a_mk_m+a_{m-1}k^{m-1}s+\cdots+a_1ks^{m-1}+a_0s^{m}=0 \tag{3}$$
and therefore
$$a_mk^m=-(a_{m-1}k^{m-1}+\cdots+a_1ks^{m-2}a_0s_{m-1})s  \tag{4}$$
and
$$a_0s^{m}=-(a_mk_{m-1}+a_{m-1}k^{m-2}s+\cdots+a_1s^{m-1})k \tag{5}$$
From $(3)$ follows $s|a_mk^m$, and because of $(2)$, we have $s|a_m$.
From $(4)$ follows $k|a_0s^{m}$ and because of $(2)$, we have $k|a_0$.
So the rational solutions $x=\frac{k}{s}$ of $(1)$ can be found by checking all possible  $k|a_0$ and $s|a_m$.
