7n^2+14n=21

Solution for 7n^2+14n=21 equation:

7n^2+14n=21

We move all terms to the left:

7n^2+14n-(21)=0

a = 7; b = 14; c = -21;
Δ = b2-4ac
Δ = 142-4·7·(-21)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-28}{2*7}=\frac{-42}{14}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+28}{2*7}=\frac{14}{14}
=1
$