(-6b-7)(5b-8)=0

Solution for (-6b-7)(5b-8)=0 equation:

(-6b-7)(5b-8)=0

We multiply parentheses ..

(-30b^2+48b-35b+56)=0

We get rid of parentheses

-30b^2+48b-35b+56=0

We add all the numbers together, and all the variables

-30b^2+13b+56=0

a = -30; b = 13; c = +56;
Δ = b2-4ac
Δ = 132-4·(-30)·56
Δ = 6889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6889}=83$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-83}{2*-30}=\frac{-96}{-60}
=1+3/5
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+83}{2*-30}=\frac{70}{-60}
=-1+1/6
$