(n*n)+(n+2)+(n-1)=100

Solution for (n*n)+(n+2)+(n-1)=100 equation:

(n*n)+(n+2)+(n-1)=100

We move all terms to the left:

(n*n)+(n+2)+(n-1)-(100)=0

We add all the numbers together, and all the variables

(+n*n)+(n+2)+(n-1)-100=0

We get rid of parentheses

n*n+n+n+2-1-100=0

We add all the numbers together, and all the variables

2n+n*n-99=0

Wy multiply elements

n^2+2n-99=0

a = 1; b = 2; c = -99;
Δ = b2-4ac
Δ = 22-4·1·(-99)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-20}{2*1}=\frac{-22}{2}
=-11
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+20}{2*1}=\frac{18}{2}
=9
$