3n+n*n=378

Solution for 3n+n*n=378 equation:

3n+n*n=378

We move all terms to the left:

3n+n*n-(378)=0

Wy multiply elements

n^2+3n-378=0

a = 1; b = 3; c = -378;
Δ = b2-4ac
Δ = 32-4·1·(-378)
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*1}=\frac{-42}{2}
=-21
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+39}{2*1}=\frac{36}{2}
=18
$