(2n+1)(n)=110

Solution for (2n+1)(n)=110 equation:

(2n+1)(n)=110

We move all terms to the left:

(2n+1)(n)-(110)=0

We multiply parentheses

2n^2+n-110=0

a = 2; b = 1; c = -110;
Δ = b2-4ac
Δ = 12-4·2·(-110)
Δ = 881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{881}}{2*2}=\frac{-1-\sqrt{881}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{881}}{2*2}=\frac{-1+\sqrt{881}}{4}
$