216=l(l+6)

Solution for 216=l(l+6) equation:

216=l(l+6)

We move all terms to the left:

216-(l(l+6))=0


We calculate terms in parentheses: -(l(l+6)), so:

l(l+6)

We multiply parentheses

l^2+6l

Back to the equation:

-(l^2+6l)


We get rid of parentheses

-l^2-6l+216=0

We add all the numbers together, and all the variables

-1l^2-6l+216=0

a = -1; b = -6; c = +216;
Δ = b2-4ac
Δ = -62-4·(-1)·216
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-30}{2*-1}=\frac{-24}{-2}
=+12
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+30}{2*-1}=\frac{36}{-2}
=-18
$