(2n-9)*n=110

Solution for (2n-9)*n=110 equation:

(2n-9)*n=110

We move all terms to the left:

(2n-9)*n-(110)=0

We multiply parentheses

2n^2-9n-110=0

a = 2; b = -9; c = -110;
Δ = b2-4ac
Δ = -92-4·2·(-110)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-31}{2*2}=\frac{-22}{4}
=-5+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+31}{2*2}=\frac{40}{4}
=10
$