-n(n+15)=54

Solution for -n(n+15)=54 equation:

-n(n+15)=54

We move all terms to the left:

-n(n+15)-(54)=0

We multiply parentheses

-n^2-15n-54=0

We add all the numbers together, and all the variables

-1n^2-15n-54=0

a = -1; b = -15; c = -54;
Δ = b2-4ac
Δ = -152-4·(-1)·(-54)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3}{2*-1}=\frac{12}{-2}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3}{2*-1}=\frac{18}{-2}
=-9
$