n(13-n)=30

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

n(13-n)=30

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-1n^2+13n-30=0

a = -1; b = 13; c = -30;
Δ = b2-4ac
Δ = 132-4·(-1)·(-30)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-7}{2*-1}=\frac{-20}{-2}
=+10
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+7}{2*-1}=\frac{-6}{-2}
=+3
$