0.25=500x-5000/500x

Solution for 0.25=500x-5000/500x equation:

0.25=500x-5000/500x

We move all terms to the left:

0.25-(500x-5000/500x)=0


Domain of the equation: 500x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+500x-5000/500x)+0.25=0

We get rid of parentheses

-500x+5000/500x+0.25=0

We multiply all the terms by the denominator


-500x*500x+(0.25)*500x+5000=0

We multiply parentheses

-500x*500x+125x+5000=0

Wy multiply elements

-250000x^2+125x+5000=0

a = -250000; b = 125; c = +5000;
Δ = b2-4ac
Δ = 1252-4·(-250000)·5000
Δ = 5000015625
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:

$\sqrt{\Delta}=\sqrt{5000015625}=\sqrt{15625*320001}=\sqrt{15625}*\sqrt{320001}=125\sqrt{320001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(125)-125\sqrt{320001}}{2*-250000}=\frac{-125-125\sqrt{320001}}{-500000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(125)+125\sqrt{320001}}{2*-250000}=\frac{-125+125\sqrt{320001}}{-500000}
$