(40+4x)(50-x)=2000

Solution for (40+4x)(50-x)=2000 equation:

(40+4x)(50-x)=2000

We move all terms to the left:

(40+4x)(50-x)-(2000)=0

We add all the numbers together, and all the variables

(4x+40)(-1x+50)-2000=0

We multiply parentheses ..

(-4x^2+200x-40x+2000)-2000=0

We get rid of parentheses

-4x^2+200x-40x+2000-2000=0

We add all the numbers together, and all the variables

-4x^2+160x=0

a = -4; b = 160; c = 0;
Δ = b2-4ac
Δ = 1602-4·(-4)·0
Δ = 25600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25600}=160$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-160}{2*-4}=\frac{-320}{-8}
=+40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+160}{2*-4}=\frac{0}{-8}
=0
$