n*n+9n-396=0

Solution for n*n+9n-396=0 equation:

n*n+9n-396=0

We add all the numbers together, and all the variables

9n+n*n-396=0

Wy multiply elements

n^2+9n-396=0

a = 1; b = 9; c = -396;
Δ = b2-4ac
Δ = 92-4·1·(-396)
Δ = 1665
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:

$\sqrt{\Delta}=\sqrt{1665}=\sqrt{9*185}=\sqrt{9}*\sqrt{185}=3\sqrt{185}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{185}}{2*1}=\frac{-9-3\sqrt{185}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{185}}{2*1}=\frac{-9+3\sqrt{185}}{2}
$