2n^2+2n=1200

Solution for 2n^2+2n=1200 equation:

2n^2+2n=1200

We move all terms to the left:

2n^2+2n-(1200)=0

a = 2; b = 2; c = -1200;
Δ = b2-4ac
Δ = 22-4·2·(-1200)
Δ = 9604
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9604}=98$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-98}{2*2}=\frac{-100}{4}
=-25
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+98}{2*2}=\frac{96}{4}
=24
$