2n+6=n2

Solution for 2n+6=n2 equation:

2n+6=n2

We move all terms to the left:

2n+6-(n2)=0

We add all the numbers together, and all the variables

-1n^2+2n+6=0

a = -1; b = 2; c = +6;
Δ = b2-4ac
Δ = 22-4·(-1)·6
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{7}}{2*-1}=\frac{-2-2\sqrt{7}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{7}}{2*-1}=\frac{-2+2\sqrt{7}}{-2}
$