(n-1)n=110

Solution for (n-1)n=110 equation:

(n-1)n=110

We move all terms to the left:

(n-1)n-(110)=0

We multiply parentheses

n^2-1n-110=0

a = 1; b = -1; c = -110;
Δ = b2-4ac
Δ = -12-4·1·(-110)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-21}{2*1}=\frac{-20}{2}
=-10
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+21}{2*1}=\frac{22}{2}
=11
$