3n2+19=382

Solution for 3n2+19=382 equation:

3n^2+19=382

We move all terms to the left:

3n^2+19-(382)=0

We add all the numbers together, and all the variables

3n^2-363=0

a = 3; b = 0; c = -363;
Δ = b2-4ac
Δ = 02-4·3·(-363)
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-66}{2*3}=\frac{-66}{6}
=-11
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+66}{2*3}=\frac{66}{6}
=11
$