(40-x)(500+100x)=45000

Solution for (40-x)(500+100x)=45000 equation:

(40-x)(500+100x)=45000

We move all terms to the left:

(40-x)(500+100x)-(45000)=0

We add all the numbers together, and all the variables

(-1x+40)(100x+500)-45000=0

We multiply parentheses ..

(-100x^2-500x+4000x+20000)-45000=0

We get rid of parentheses

-100x^2-500x+4000x+20000-45000=0

We add all the numbers together, and all the variables

-100x^2+3500x-25000=0

a = -100; b = 3500; c = -25000;
Δ = b2-4ac
Δ = 35002-4·(-100)·(-25000)
Δ = 2250000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2250000}=1500$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3500)-1500}{2*-100}=\frac{-5000}{-200}
=+25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3500)+1500}{2*-100}=\frac{-2000}{-200}
=+10
$