3n^2+19=363

Solution for 3n^2+19=363 equation:

3n^2+19=363

We move all terms to the left:

3n^2+19-(363)=0

We add all the numbers together, and all the variables

3n^2-344=0

a = 3; b = 0; c = -344;
Δ = b2-4ac
Δ = 02-4·3·(-344)
Δ = 4128
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:

$\sqrt{\Delta}=\sqrt{4128}=\sqrt{16*258}=\sqrt{16}*\sqrt{258}=4\sqrt{258}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{258}}{2*3}=\frac{0-4\sqrt{258}}{6}
=-\frac{4\sqrt{258}}{6}
=-\frac{2\sqrt{258}}{3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{258}}{2*3}=\frac{0+4\sqrt{258}}{6}
=\frac{4\sqrt{258}}{6}
=\frac{2\sqrt{258}}{3}
$