(l-3)(l-2)=30

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

(l-3)(l-2)=30

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

l^2-5l-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:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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