(2x+40)*(2x+20)=900

Solution for (2x+40)*(2x+20)=900 equation:

(2x+40)(2x+20)=900

We move all terms to the left:

(2x+40)(2x+20)-(900)=0

We multiply parentheses ..

(+4x^2+40x+80x+800)-900=0

We get rid of parentheses

4x^2+40x+80x+800-900=0

We add all the numbers together, and all the variables

4x^2+120x-100=0

a = 4; b = 120; c = -100;
Δ = b2-4ac
Δ = 1202-4·4·(-100)
Δ = 16000
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:

$\sqrt{\Delta}=\sqrt{16000}=\sqrt{1600*10}=\sqrt{1600}*\sqrt{10}=40\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-40\sqrt{10}}{2*4}=\frac{-120-40\sqrt{10}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+40\sqrt{10}}{2*4}=\frac{-120+40\sqrt{10}}{8}
$