40000=x-5000/x

Solution for 40000=x-5000/x equation:

40000=x-5000/x

We move all terms to the left:

40000-(x-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)+40000=0

We get rid of parentheses

-x+5000/x+40000=0

We multiply all the terms by the denominator


-x*x+40000*x+5000=0

We add all the numbers together, and all the variables

40000x-x*x+5000=0

Wy multiply elements

-1x^2+40000x+5000=0

a = -1; b = 40000; c = +5000;
Δ = b2-4ac
Δ = 400002-4·(-1)·5000
Δ = 1600020000
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:

$\sqrt{\Delta}=\sqrt{1600020000}=\sqrt{90000*17778}=\sqrt{90000}*\sqrt{17778}=300\sqrt{17778}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40000)-300\sqrt{17778}}{2*-1}=\frac{-40000-300\sqrt{17778}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40000)+300\sqrt{17778}}{2*-1}=\frac{-40000+300\sqrt{17778}}{-2}
$