n2+2n=74

Solution for n2+2n=74 equation:

n2+2n=74

We move all terms to the left:

n2+2n-(74)=0

We add all the numbers together, and all the variables

n^2+2n-74=0

a = 1; b = 2; c = -74;
Δ = b2-4ac
Δ = 22-4·1·(-74)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10\sqrt{3}}{2*1}=\frac{-2-10\sqrt{3}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10\sqrt{3}}{2*1}=\frac{-2+10\sqrt{3}}{2}
$