n^2-2n-378=0

Solution for n^2-2n-378=0 equation:

n^2-2n-378=0

a = 1; b = -2; c = -378;
Δ = b2-4ac
Δ = -22-4·1·(-378)
Δ = 1516
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1516}=\sqrt{4*379}=\sqrt{4}*\sqrt{379}=2\sqrt{379}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{379}}{2*1}=\frac{2-2\sqrt{379}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{379}}{2*1}=\frac{2+2\sqrt{379}}{2}
$