(n-2)(n-3)=30

Solution for (n-2)(n-3)=30 equation:

(n-2)(n-3)=30

We move all terms to the left:

(n-2)(n-3)-(30)=0

We multiply parentheses ..

(+n^2-3n-2n+6)-30=0

We get rid of parentheses

n^2-3n-2n+6-30=0

We add all the numbers together, and all the variables

n^2-5n-24=0

a = 1; b = -5; c = -24;
Δ = b2-4ac
Δ = -52-4·1·(-24)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*1}=\frac{-6}{2}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*1}=\frac{16}{2}
=8
$