(n+1)(n+2)=90

Solution for (n+1)(n+2)=90 equation:

(n+1)(n+2)=90

We move all terms to the left:

(n+1)(n+2)-(90)=0

We multiply parentheses ..

(+n^2+2n+n+2)-90=0

We get rid of parentheses

n^2+2n+n+2-90=0

We add all the numbers together, and all the variables

n^2+3n-88=0

a = 1; b = 3; c = -88;
Δ = b2-4ac
Δ = 32-4·1·(-88)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-19}{2*1}=\frac{-22}{2}
=-11
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+19}{2*1}=\frac{16}{2}
=8
$