n^2=11n+126

Solution for n^2=11n+126 equation:

n^2=11n+126

We move all terms to the left:

n^2-(11n+126)=0

We get rid of parentheses

n^2-11n-126=0

a = 1; b = -11; c = -126;
Δ = b2-4ac
Δ = -112-4·1·(-126)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-25}{2*1}=\frac{-14}{2}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+25}{2*1}=\frac{36}{2}
=18
$