(2x+40)(x+20)=180

Solution for (2x+40)(x+20)=180 equation:

(2x+40)(x+20)=180

We move all terms to the left:

(2x+40)(x+20)-(180)=0

We multiply parentheses ..

(+2x^2+40x+40x+800)-180=0

We get rid of parentheses

2x^2+40x+40x+800-180=0

We add all the numbers together, and all the variables

2x^2+80x+620=0

a = 2; b = 80; c = +620;
Δ = b2-4ac
Δ = 802-4·2·620
Δ = 1440
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-12\sqrt{10}}{2*2}=\frac{-80-12\sqrt{10}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+12\sqrt{10}}{2*2}=\frac{-80+12\sqrt{10}}{4}
$