n(-13-n)=36

Solution for n(-13-n)=36 equation:

n(-13-n)=36

We move all terms to the left:

n(-13-n)-(36)=0

We add all the numbers together, and all the variables

n(-1n-13)-36=0

We multiply parentheses

-1n^2-13n-36=0

a = -1; b = -13; c = -36;
Δ = b2-4ac
Δ = -132-4·(-1)·(-36)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-5}{2*-1}=\frac{8}{-2}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+5}{2*-1}=\frac{18}{-2}
=-9
$