n^2-n=2n+18

Solution for n^2-n=2n+18 equation:

n^2-n=2n+18

We move all terms to the left:

n^2-n-(2n+18)=0

We add all the numbers together, and all the variables

n^2-1n-(2n+18)=0

We get rid of parentheses

n^2-1n-2n-18=0

We add all the numbers together, and all the variables

n^2-3n-18=0

a = 1; b = -3; c = -18;
Δ = b2-4ac
Δ = -32-4·1·(-18)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-9}{2*1}=\frac{-6}{2}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+9}{2*1}=\frac{12}{2}
=6
$