(2x+40)*(2x+30)=2000

Solution for (2x+40)*(2x+30)=2000 equation:

(2x+40)(2x+30)=2000

We move all terms to the left:

(2x+40)(2x+30)-(2000)=0

We multiply parentheses ..

(+4x^2+60x+80x+1200)-2000=0

We get rid of parentheses

4x^2+60x+80x+1200-2000=0

We add all the numbers together, and all the variables

4x^2+140x-800=0

a = 4; b = 140; c = -800;
Δ = b2-4ac
Δ = 1402-4·4·(-800)
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-180}{2*4}=\frac{-320}{8}
=-40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+180}{2*4}=\frac{40}{8}
=5
$