(13-n)(12-n)=30

Solution for (13-n)(12-n)=30 equation:

(13-n)(12-n)=30

We move all terms to the left:

(13-n)(12-n)-(30)=0

We add all the numbers together, and all the variables

(-1n+13)(-1n+12)-30=0

We multiply parentheses ..

(+n^2-12n-13n+156)-30=0

We get rid of parentheses

n^2-12n-13n+156-30=0

We add all the numbers together, and all the variables

n^2-25n+126=0

a = 1; b = -25; c = +126;
Δ = b2-4ac
Δ = -252-4·1·126
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-11}{2*1}=\frac{14}{2}
=7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+11}{2*1}=\frac{36}{2}
=18
$