60000/(x-2)=60000/x+250

Solution for 60000/(x-2)=60000/x+250 equation:

60000/(x-2)=60000/x+250

We move all terms to the left:

60000/(x-2)-(60000/x+250)=0


Domain of the equation: (x-2)!=0

We move all terms containing x to the left, all other terms to the right

x!=2

x∈R



Domain of the equation: x+250)!=0

x∈R


We get rid of parentheses

60000/(x-2)-60000/x-250=0

We calculate fractions


60000x/(x^2-2x)+(-60000x+120000)/(x^2-2x)-250=0

We multiply all the terms by the denominator


60000x+(-60000x+120000)-250*(x^2-2x)=0

We multiply parentheses

-250x^2+60000x+(-60000x+120000)+500x=0

We get rid of parentheses

-250x^2+60000x-60000x+500x+120000=0

We add all the numbers together, and all the variables

-250x^2+500x+120000=0

a = -250; b = 500; c = +120000;
Δ = b2-4ac
Δ = 5002-4·(-250)·120000
Δ = 120250000
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:

$\sqrt{\Delta}=\sqrt{120250000}=\sqrt{250000*481}=\sqrt{250000}*\sqrt{481}=500\sqrt{481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(500)-500\sqrt{481}}{2*-250}=\frac{-500-500\sqrt{481}}{-500}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(500)+500\sqrt{481}}{2*-250}=\frac{-500+500\sqrt{481}}{-500}
$