n^2+6n=13

Solution for n^2+6n=13 equation:

n^2+6n=13

We move all terms to the left:

n^2+6n-(13)=0

a = 1; b = 6; c = -13;
Δ = b2-4ac
Δ = 62-4·1·(-13)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{22}}{2*1}=\frac{-6-2\sqrt{22}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{22}}{2*1}=\frac{-6+2\sqrt{22}}{2}
$