-84n-n^2=-5292

Solution for -84n-n^2=-5292 equation:

-84n-n^2=-5292

We move all terms to the left:

-84n-n^2-(-5292)=0

We add all the numbers together, and all the variables

-1n^2-84n+5292=0

a = -1; b = -84; c = +5292;
Δ = b2-4ac
Δ = -842-4·(-1)·5292
Δ = 28224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28224}=168$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-168}{2*-1}=\frac{-84}{-2}
=+42
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+168}{2*-1}=\frac{252}{-2}
=-126
$