n^2+84*n=100

Solution for n^2+84*n=100 equation:

n^2+84n=100

We move all terms to the left:

n^2+84n-(100)=0

a = 1; b = 84; c = -100;
Δ = b2-4ac
Δ = 842-4·1·(-100)
Δ = 7456
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:

$\sqrt{\Delta}=\sqrt{7456}=\sqrt{16*466}=\sqrt{16}*\sqrt{466}=4\sqrt{466}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{466}}{2*1}=\frac{-84-4\sqrt{466}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{466}}{2*1}=\frac{-84+4\sqrt{466}}{2}
$