7n^2+21n=126

Solution for 7n^2+21n=126 equation:

7n^2+21n=126

We move all terms to the left:

7n^2+21n-(126)=0

a = 7; b = 21; c = -126;
Δ = b2-4ac
Δ = 212-4·7·(-126)
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-63}{2*7}=\frac{-84}{14}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+63}{2*7}=\frac{42}{14}
=3
$