60=2x+200/x

Solution for 60=2x+200/x equation:

60=2x+200/x

We move all terms to the left:

60-(2x+200/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

-(+2x+200/x)+60=0

We get rid of parentheses

-2x-200/x+60=0

We multiply all the terms by the denominator


-2x*x+60*x-200=0

We add all the numbers together, and all the variables

60x-2x*x-200=0

Wy multiply elements

-2x^2+60x-200=0

a = -2; b = 60; c = -200;
Δ = b2-4ac
Δ = 602-4·(-2)·(-200)
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{-(60)-20\sqrt{5}}{2*-2}=\frac{-60-20\sqrt{5}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+20\sqrt{5}}{2*-2}=\frac{-60+20\sqrt{5}}{-4}
$