3n^2+3n=126

Solution for 3n^2+3n=126 equation:

3n^2+3n=126

We move all terms to the left:

3n^2+3n-(126)=0

a = 3; b = 3; c = -126;
Δ = b2-4ac
Δ = 32-4·3·(-126)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-39}{2*3}=\frac{-42}{6}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+39}{2*3}=\frac{36}{6}
=6
$