(n-5)(n-6)=9

Solution for (n-5)(n-6)=9 equation:

(n-5)(n-6)=9

We move all terms to the left:

(n-5)(n-6)-(9)=0

We multiply parentheses ..

(+n^2-6n-5n+30)-9=0

We get rid of parentheses

n^2-6n-5n+30-9=0

We add all the numbers together, and all the variables

n^2-11n+21=0

a = 1; b = -11; c = +21;
Δ = b2-4ac
Δ = -112-4·1·21
Δ = 37
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{37}}{2*1}=\frac{11-\sqrt{37}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{37}}{2*1}=\frac{11+\sqrt{37}}{2}
$