11n+3n^2=484

Solution for 11n+3n^2=484 equation:

11n+3n^2=484

We move all terms to the left:

11n+3n^2-(484)=0

a = 3; b = 11; c = -484;
Δ = b2-4ac
Δ = 112-4·3·(-484)
Δ = 5929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5929}=77$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-77}{2*3}=\frac{-88}{6}
=-14+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+77}{2*3}=\frac{66}{6}
=11
$