(7y-6)(-5y-9)=0

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

(7y-6)(-5y-9)=0

We multiply parentheses ..

(-35y^2-63y+30y+54)=0

We get rid of parentheses

-35y^2-63y+30y+54=0

We add all the numbers together, and all the variables

-35y^2-33y+54=0

a = -35; b = -33; c = +54;
Δ = b2-4ac
Δ = -332-4·(-35)·54
Δ = 8649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8649}=93$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-93}{2*-35}=\frac{-60}{-70}
=6/7
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+93}{2*-35}=\frac{126}{-70}
=-1+4/5
$