100=l(l-15)

Solution for 100=l(l-15) equation:

100=l(l-15)

We move all terms to the left:

100-(l(l-15))=0


We calculate terms in parentheses: -(l(l-15)), so:

l(l-15)

We multiply parentheses

l^2-15l

Back to the equation:

-(l^2-15l)


We get rid of parentheses

-l^2+15l+100=0

We add all the numbers together, and all the variables

-1l^2+15l+100=0

a = -1; b = 15; c = +100;
Δ = b2-4ac
Δ = 152-4·(-1)·100
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-25}{2*-1}=\frac{-40}{-2}
=+20
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+25}{2*-1}=\frac{10}{-2}
=-5
$