2000=x+1/x

Solution for 2000=x+1/x equation:

2000=x+1/x

We move all terms to the left:

2000-(x+1/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+1/x)+2000=0

We get rid of parentheses

-x-1/x+2000=0

We multiply all the terms by the denominator


-x*x+2000*x-1=0

We add all the numbers together, and all the variables

2000x-x*x-1=0

Wy multiply elements

-1x^2+2000x-1=0

a = -1; b = 2000; c = -1;
Δ = b2-4ac
Δ = 20002-4·(-1)·(-1)
Δ = 3999996
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:

$\sqrt{\Delta}=\sqrt{3999996}=\sqrt{36*111111}=\sqrt{36}*\sqrt{111111}=6\sqrt{111111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2000)-6\sqrt{111111}}{2*-1}=\frac{-2000-6\sqrt{111111}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2000)+6\sqrt{111111}}{2*-1}=\frac{-2000+6\sqrt{111111}}{-2}
$