n^2-13=n

Solution for n^2-13=n equation:

n^2-13=n

We move all terms to the left:

n^2-13-(n)=0

We add all the numbers together, and all the variables

n^2-1n-13=0

a = 1; b = -1; c = -13;
Δ = b2-4ac
Δ = -12-4·1·(-13)
Δ = 53
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{-(-1)-\sqrt{53}}{2*1}=\frac{1-\sqrt{53}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{53}}{2*1}=\frac{1+\sqrt{53}}{2}
$