X+8000/x+4000/x=30000

Solution for X+8000/x+4000/x=30000 equation:

X+8000/X+4000/X=30000

We move all terms to the left:

X+8000/X+4000/X-(30000)=0


Domain of the equation: X!=0

X∈R


We multiply all the terms by the denominator


X*X-30000*X+8000+4000=0

We add all the numbers together, and all the variables

-30000X+X*X+12000=0

Wy multiply elements

X^2-30000X+12000=0

a = 1; b = -30000; c = +12000;
Δ = b2-4ac
Δ = -300002-4·1·12000
Δ = 899952000
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:

$\sqrt{\Delta}=\sqrt{899952000}=\sqrt{1600*562470}=\sqrt{1600}*\sqrt{562470}=40\sqrt{562470}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30000)-40\sqrt{562470}}{2*1}=\frac{30000-40\sqrt{562470}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30000)+40\sqrt{562470}}{2*1}=\frac{30000+40\sqrt{562470}}{2}
$