7=n2+2n

Solution for 7=n2+2n equation:

7=n2+2n

We move all terms to the left:

7-(n2+2n)=0

We add all the numbers together, and all the variables

-(+n^2+2n)+7=0

We get rid of parentheses

-n^2-2n+7=0

We add all the numbers together, and all the variables

-1n^2-2n+7=0

a = -1; b = -2; c = +7;
Δ = b2-4ac
Δ = -22-4·(-1)·7
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{2}}{2*-1}=\frac{2-4\sqrt{2}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{2}}{2*-1}=\frac{2+4\sqrt{2}}{-2}
$