(-6x+5)(-7x-9)=0

Solution for (-6x+5)(-7x-9)=0 equation:

(-6x+5)(-7x-9)=0

We multiply parentheses ..

(+42x^2+54x-35x-45)=0

We get rid of parentheses

42x^2+54x-35x-45=0

We add all the numbers together, and all the variables

42x^2+19x-45=0

a = 42; b = 19; c = -45;
Δ = b2-4ac
Δ = 192-4·42·(-45)
Δ = 7921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7921}=89$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-89}{2*42}=\frac{-108}{84}
=-1+2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+89}{2*42}=\frac{70}{84}
=5/6
$