2x+1000/x=100

Solution for 2x+1000/x=100 equation:

2x+1000/x=100

We move all terms to the left:

2x+1000/x-(100)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


2x*x-100*x+1000=0

We add all the numbers together, and all the variables

-100x+2x*x+1000=0

Wy multiply elements

2x^2-100x+1000=0

a = 2; b = -100; c = +1000;
Δ = b2-4ac
Δ = -1002-4·2·1000
Δ = 2000
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:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{5}}{2*2}=\frac{100-20\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{5}}{2*2}=\frac{100+20\sqrt{5}}{4}
$