3n^2+303-16200=0

Solution for 3n^2+303-16200=0 equation:

3n^2+303-16200=0

We add all the numbers together, and all the variables

3n^2-15897=0

a = 3; b = 0; c = -15897;
Δ = b2-4ac
Δ = 02-4·3·(-15897)
Δ = 190764
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:

$\sqrt{\Delta}=\sqrt{190764}=\sqrt{36*5299}=\sqrt{36}*\sqrt{5299}=6\sqrt{5299}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5299}}{2*3}=\frac{0-6\sqrt{5299}}{6}
=-\frac{6\sqrt{5299}}{6}
=-\sqrt{5299}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5299}}{2*3}=\frac{0+6\sqrt{5299}}{6}
=\frac{6\sqrt{5299}}{6}
=\sqrt{5299}
$