n*3n=399

Solution for n*3n=399 equation:

n*3n=399

We move all terms to the left:

n*3n-(399)=0

Wy multiply elements

3n^2-399=0

a = 3; b = 0; c = -399;
Δ = b2-4ac
Δ = 02-4·3·(-399)
Δ = 4788
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:

$\sqrt{\Delta}=\sqrt{4788}=\sqrt{36*133}=\sqrt{36}*\sqrt{133}=6\sqrt{133}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{133}}{2*3}=\frac{0-6\sqrt{133}}{6}
=-\frac{6\sqrt{133}}{6}
=-\sqrt{133}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{133}}{2*3}=\frac{0+6\sqrt{133}}{6}
=\frac{6\sqrt{133}}{6}
=\sqrt{133}
$