200+2x=240/x+x

Solution for 200+2x=240/x+x equation:

200+2x=240/x+x

We move all terms to the left:

200+2x-(240/x+x)=0


Domain of the equation: x+x)!=0

x∈R


We add all the numbers together, and all the variables

2x-(+x+240/x)+200=0

We get rid of parentheses

2x-x-240/x+200=0

We multiply all the terms by the denominator


2x*x-x*x+200*x-240=0

We add all the numbers together, and all the variables

200x+2x*x-x*x-240=0

Wy multiply elements

2x^2-1x^2+200x-240=0

We add all the numbers together, and all the variables

x^2+200x-240=0

a = 1; b = 200; c = -240;
Δ = b2-4ac
Δ = 2002-4·1·(-240)
Δ = 40960
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:

$\sqrt{\Delta}=\sqrt{40960}=\sqrt{4096*10}=\sqrt{4096}*\sqrt{10}=64\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-64\sqrt{10}}{2*1}=\frac{-200-64\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+64\sqrt{10}}{2*1}=\frac{-200+64\sqrt{10}}{2}
$