7n^2+21n-378=0

Solution for 7n^2+21n-378=0 equation:

7n^2+21n-378=0

a = 7; b = 21; c = -378;
Δ = b2-4ac
Δ = 212-4·7·(-378)
Δ = 11025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11025}=105$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-105}{2*7}=\frac{-126}{14}
=-9
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+105}{2*7}=\frac{84}{14}
=6
$