x+(2100/x)=1200

Solution for x+(2100/x)=1200 equation:

x+(2100/x)=1200

We move all terms to the left:

x+(2100/x)-(1200)=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+(+2100/x)-1200=0

We get rid of parentheses

x+2100/x-1200=0

We multiply all the terms by the denominator


x*x-1200*x+2100=0

We add all the numbers together, and all the variables

-1200x+x*x+2100=0

Wy multiply elements

x^2-1200x+2100=0

a = 1; b = -1200; c = +2100;
Δ = b2-4ac
Δ = -12002-4·1·2100
Δ = 1431600
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:

$\sqrt{\Delta}=\sqrt{1431600}=\sqrt{400*3579}=\sqrt{400}*\sqrt{3579}=20\sqrt{3579}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1200)-20\sqrt{3579}}{2*1}=\frac{1200-20\sqrt{3579}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1200)+20\sqrt{3579}}{2*1}=\frac{1200+20\sqrt{3579}}{2}
$