24000=(24000/x-200)(x+4)

Solution for 24000=(24000/x-200)(x+4) equation:

24000=(24000/x-200)(x+4)

We move all terms to the left:

24000-((24000/x-200)(x+4))=0


Domain of the equation: x-200)(x+4))!=0

x∈R


We multiply parentheses ..

-((+24000x^2+96000x-200x-800))+24000=0


We calculate terms in parentheses: -((+24000x^2+96000x-200x-800)), so:

(+24000x^2+96000x-200x-800)

We get rid of parentheses

24000x^2+96000x-200x-800

We add all the numbers together, and all the variables

24000x^2+95800x-800

Back to the equation:

-(24000x^2+95800x-800)


We get rid of parentheses

-24000x^2-95800x+800+24000=0

We add all the numbers together, and all the variables

-24000x^2-95800x+24800=0

a = -24000; b = -95800; c = +24800;
Δ = b2-4ac
Δ = -958002-4·(-24000)·24800
Δ = 11558440000
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:

$\sqrt{\Delta}=\sqrt{11558440000}=\sqrt{40000*288961}=\sqrt{40000}*\sqrt{288961}=200\sqrt{288961}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-95800)-200\sqrt{288961}}{2*-24000}=\frac{95800-200\sqrt{288961}}{-48000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-95800)+200\sqrt{288961}}{2*-24000}=\frac{95800+200\sqrt{288961}}{-48000}
$