2n2-105=-11n

Solution for 2n2-105=-11n equation:

2n^2-105=-11n

We move all terms to the left:

2n^2-105-(-11n)=0

We get rid of parentheses

2n^2+11n-105=0

a = 2; b = 11; c = -105;
Δ = b2-4ac
Δ = 112-4·2·(-105)
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{-(11)-31}{2*2}=\frac{-42}{4}
=-10+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+31}{2*2}=\frac{20}{4}
=5
$