x+(100/x)=110

Solution for x+(100/x)=110 equation:

x+(100/x)=110

We move all terms to the left:

x+(100/x)-(110)=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+(+100/x)-110=0

We get rid of parentheses

x+100/x-110=0

We multiply all the terms by the denominator


x*x-110*x+100=0

We add all the numbers together, and all the variables

-110x+x*x+100=0

Wy multiply elements

x^2-110x+100=0

a = 1; b = -110; c = +100;
Δ = b2-4ac
Δ = -1102-4·1·100
Δ = 11700
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:

$\sqrt{\Delta}=\sqrt{11700}=\sqrt{900*13}=\sqrt{900}*\sqrt{13}=30\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-30\sqrt{13}}{2*1}=\frac{110-30\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+30\sqrt{13}}{2*1}=\frac{110+30\sqrt{13}}{2}
$