x+100/x=500

Solution for x+100/x=500 equation:

x+100/x=500

We move all terms to the left:

x+100/x-(500)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-500*x+100=0

We add all the numbers together, and all the variables

-500x+x*x+100=0

Wy multiply elements

x^2-500x+100=0

a = 1; b = -500; c = +100;
Δ = b2-4ac
Δ = -5002-4·1·100
Δ = 249600
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:

$\sqrt{\Delta}=\sqrt{249600}=\sqrt{6400*39}=\sqrt{6400}*\sqrt{39}=80\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-80\sqrt{39}}{2*1}=\frac{500-80\sqrt{39}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+80\sqrt{39}}{2*1}=\frac{500+80\sqrt{39}}{2}
$