(6n-6)(7n-8)=0

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

(6n-6)(7n-8)=0

We multiply parentheses ..

(+42n^2-48n-42n+48)=0

We get rid of parentheses

42n^2-48n-42n+48=0

We add all the numbers together, and all the variables

42n^2-90n+48=0

a = 42; b = -90; c = +48;
Δ = b2-4ac
Δ = -902-4·42·48
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6}{2*42}=\frac{84}{84}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6}{2*42}=\frac{96}{84}
=1+1/7
$