(n-2)(n+3)=6

Solution for (n-2)(n+3)=6 equation:

(n-2)(n+3)=6

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

n^2+n-12=0

a = 1; b = 1; c = -12;
Δ = b2-4ac
Δ = 12-4·1·(-12)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*1}=\frac{-8}{2}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*1}=\frac{6}{2}
=3
$