n^2+84*n=81

Solution for n^2+84*n=81 equation:

n^2+84n=81

We move all terms to the left:

n^2+84n-(81)=0

a = 1; b = 84; c = -81;
Δ = b2-4ac
Δ = 842-4·1·(-81)
Δ = 7380
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7380}=\sqrt{36*205}=\sqrt{36}*\sqrt{205}=6\sqrt{205}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-6\sqrt{205}}{2*1}=\frac{-84-6\sqrt{205}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+6\sqrt{205}}{2*1}=\frac{-84+6\sqrt{205}}{2}
$