x=490-5000/x

Solution for x=490-5000/x equation:

x=490-5000/x

We move all terms to the left:

x-(490-5000/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-(-5000/x+490)=0

We get rid of parentheses

x+5000/x-490=0

We multiply all the terms by the denominator


x*x-490*x+5000=0

We add all the numbers together, and all the variables

-490x+x*x+5000=0

Wy multiply elements

x^2-490x+5000=0

a = 1; b = -490; c = +5000;
Δ = b2-4ac
Δ = -4902-4·1·5000
Δ = 220100
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:

$\sqrt{\Delta}=\sqrt{220100}=\sqrt{100*2201}=\sqrt{100}*\sqrt{2201}=10\sqrt{2201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-490)-10\sqrt{2201}}{2*1}=\frac{490-10\sqrt{2201}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-490)+10\sqrt{2201}}{2*1}=\frac{490+10\sqrt{2201}}{2}
$