n^2-18n-21=5

Solution for n^2-18n-21=5 equation:

n^2-18n-21=5

We move all terms to the left:

n^2-18n-21-(5)=0

We add all the numbers together, and all the variables

n^2-18n-26=0

a = 1; b = -18; c = -26;
Δ = b2-4ac
Δ = -182-4·1·(-26)
Δ = 428
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:

$\sqrt{\Delta}=\sqrt{428}=\sqrt{4*107}=\sqrt{4}*\sqrt{107}=2\sqrt{107}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{107}}{2*1}=\frac{18-2\sqrt{107}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{107}}{2*1}=\frac{18+2\sqrt{107}}{2}
$