n(2)-8=2n+20

Solution for n(2)-8=2n+20 equation:

n(2)-8=2n+20

We move all terms to the left:

n(2)-8-(2n+20)=0

We add all the numbers together, and all the variables

n^2-(2n+20)-8=0

We get rid of parentheses

n^2-2n-20-8=0

We add all the numbers together, and all the variables

n^2-2n-28=0

a = 1; b = -2; c = -28;
Δ = b2-4ac
Δ = -22-4·1·(-28)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{29}}{2*1}=\frac{2-2\sqrt{29}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{29}}{2*1}=\frac{2+2\sqrt{29}}{2}
$