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

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

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

We multiply parentheses ..

(+n^2-7n-6n+42)=0

We get rid of parentheses

n^2-7n-6n+42=0

We add all the numbers together, and all the variables

n^2-13n+42=0

a = 1; b = -13; c = +42;
Δ = b2-4ac
Δ = -132-4·1·42
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-1}{2*1}=\frac{12}{2}
=6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+1}{2*1}=\frac{14}{2}
=7
$