100x=500/x

Solution for 100x=500/x equation:

100x=500/x

We move all terms to the left:

100x-(500/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

100x-(+500/x)=0

We get rid of parentheses

100x-500/x=0

We multiply all the terms by the denominator


100x*x-500=0

Wy multiply elements

100x^2-500=0

a = 100; b = 0; c = -500;
Δ = b2-4ac
Δ = 02-4·100·(-500)
Δ = 200000
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:

$\sqrt{\Delta}=\sqrt{200000}=\sqrt{40000*5}=\sqrt{40000}*\sqrt{5}=200\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{5}}{2*100}=\frac{0-200\sqrt{5}}{200}
=-\frac{200\sqrt{5}}{200}
=-\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{5}}{2*100}=\frac{0+200\sqrt{5}}{200}
=\frac{200\sqrt{5}}{200}
=\sqrt{5}
$