100=x+2/x

Solution for 100=x+2/x equation:

100=x+2/x

We move all terms to the left:

100-(x+2/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+2/x)+100=0

We get rid of parentheses

-x-2/x+100=0

We multiply all the terms by the denominator


-x*x+100*x-2=0

We add all the numbers together, and all the variables

100x-x*x-2=0

Wy multiply elements

-1x^2+100x-2=0

a = -1; b = 100; c = -2;
Δ = b2-4ac
Δ = 1002-4·(-1)·(-2)
Δ = 9992
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:

$\sqrt{\Delta}=\sqrt{9992}=\sqrt{4*2498}=\sqrt{4}*\sqrt{2498}=2\sqrt{2498}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-2\sqrt{2498}}{2*-1}=\frac{-100-2\sqrt{2498}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+2\sqrt{2498}}{2*-1}=\frac{-100+2\sqrt{2498}}{-2}
$