2n^2+4n=510

Solution for 2n^2+4n=510 equation:

2n^2+4n=510

We move all terms to the left:

2n^2+4n-(510)=0

a = 2; b = 4; c = -510;
Δ = b2-4ac
Δ = 42-4·2·(-510)
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-64}{2*2}=\frac{-68}{4}
=-17
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+64}{2*2}=\frac{60}{4}
=15
$