13n+2=n^2

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

13n+2=n^2

We move all terms to the left:

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

determiningTheFunctionDomain
-n^2+13n+2=0

We add all the numbers together, and all the variables

-1n^2+13n+2=0

a = -1; b = 13; c = +2;
Δ = b2-4ac
Δ = 132-4·(-1)·2
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{177}}{2*-1}=\frac{-13-\sqrt{177}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{177}}{2*-1}=\frac{-13+\sqrt{177}}{-2}
$