2n^2-138=11n

Solution for 2n^2-138=11n equation:

2n^2-138=11n

We move all terms to the left:

2n^2-138-(11n)=0

a = 2; b = -11; c = -138;
Δ = b2-4ac
Δ = -112-4·2·(-138)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-35}{2*2}=\frac{-24}{4}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+35}{2*2}=\frac{46}{4}
=11+1/2
$