1000/x+2x=200

Solution for 1000/x+2x=200 equation:

1000/x+2x=200

We move all terms to the left:

1000/x+2x-(200)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x+1000/x-200=0

We multiply all the terms by the denominator


2x*x-200*x+1000=0

We add all the numbers together, and all the variables

-200x+2x*x+1000=0

Wy multiply elements

2x^2-200x+1000=0

a = 2; b = -200; c = +1000;
Δ = b2-4ac
Δ = -2002-4·2·1000
Δ = 32000
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:

$\sqrt{\Delta}=\sqrt{32000}=\sqrt{6400*5}=\sqrt{6400}*\sqrt{5}=80\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-80\sqrt{5}}{2*2}=\frac{200-80\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+80\sqrt{5}}{2*2}=\frac{200+80\sqrt{5}}{4}
$