(4l+60)(l+20)=180

Solution for (4l+60)(l+20)=180 equation:

(4l+60)(l+20)=180

We move all terms to the left:

(4l+60)(l+20)-(180)=0

We multiply parentheses ..

(+4l^2+80l+60l+1200)-180=0

We get rid of parentheses

4l^2+80l+60l+1200-180=0

We add all the numbers together, and all the variables

4l^2+140l+1020=0

a = 4; b = 140; c = +1020;
Δ = b2-4ac
Δ = 1402-4·4·1020
Δ = 3280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3280}=\sqrt{16*205}=\sqrt{16}*\sqrt{205}=4\sqrt{205}$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-4\sqrt{205}}{2*4}=\frac{-140-4\sqrt{205}}{8}
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+4\sqrt{205}}{2*4}=\frac{-140+4\sqrt{205}}{8}
$