l(l-5)=84

Solution for l(l-5)=84 equation:

l(l-5)=84

We move all terms to the left:

l(l-5)-(84)=0

We multiply parentheses

l^2-5l-84=0

a = 1; b = -5; c = -84;
Δ = b2-4ac
Δ = -52-4·1·(-84)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-19}{2*1}=\frac{-14}{2}
=-7
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+19}{2*1}=\frac{24}{2}
=12
$