n^2+84*n=1

Solution for n^2+84*n=1 equation:

n^2+84n=1

We move all terms to the left:

n^2+84n-(1)=0

a = 1; b = 84; c = -1;
Δ = b2-4ac
Δ = 842-4·1·(-1)
Δ = 7060
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:

$\sqrt{\Delta}=\sqrt{7060}=\sqrt{4*1765}=\sqrt{4}*\sqrt{1765}=2\sqrt{1765}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-2\sqrt{1765}}{2*1}=\frac{-84-2\sqrt{1765}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+2\sqrt{1765}}{2*1}=\frac{-84+2\sqrt{1765}}{2}
$