500x=400/x

Solution for 500x=400/x equation:

500x=400/x

We move all terms to the left:

500x-(400/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

500x-(+400/x)=0

We get rid of parentheses

500x-400/x=0

We multiply all the terms by the denominator


500x*x-400=0

Wy multiply elements

500x^2-400=0

a = 500; b = 0; c = -400;
Δ = b2-4ac
Δ = 02-4·500·(-400)
Δ = 800000
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:

$\sqrt{\Delta}=\sqrt{800000}=\sqrt{160000*5}=\sqrt{160000}*\sqrt{5}=400\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-400\sqrt{5}}{2*500}=\frac{0-400\sqrt{5}}{1000}
=-\frac{400\sqrt{5}}{1000}
=-\frac{2\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+400\sqrt{5}}{2*500}=\frac{0+400\sqrt{5}}{1000}
=\frac{400\sqrt{5}}{1000}
=\frac{2\sqrt{5}}{5}
$