0.2=x-200000/x

Solution for 0.2=x-200000/x equation:

0.2=x-200000/x

We move all terms to the left:

0.2-(x-200000/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x-200000/x)+0.2=0

We get rid of parentheses

-x+200000/x+0.2=0

We multiply all the terms by the denominator


-x*x+(0.2)*x+200000=0

We multiply parentheses

-x*x+0.2x+200000=0

Wy multiply elements

-1x^2+0.2x+200000=0

a = -1; b = 0.2; c = +200000;
Δ = b2-4ac
Δ = 0.22-4·(-1)·200000
Δ = 800000.04
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.2)-\sqrt{800000.04}}{2*-1}=\frac{-0.2-\sqrt{800000.04}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.2)+\sqrt{800000.04}}{2*-1}=\frac{-0.2+\sqrt{800000.04}}{-2}
$