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

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

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

We multiply parentheses ..

(+7n^2-7n-56n+56)=0

We get rid of parentheses

7n^2-7n-56n+56=0

We add all the numbers together, and all the variables

7n^2-63n+56=0

a = 7; b = -63; c = +56;
Δ = b2-4ac
Δ = -632-4·7·56
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-49}{2*7}=\frac{14}{14}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+49}{2*7}=\frac{112}{14}
=8
$