(100/x)+x=37

Solution for (100/x)+x=37 equation:

(100/x)+x=37

We move all terms to the left:

(100/x)+x-(37)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+100/x)+x-37=0

We add all the numbers together, and all the variables

x+(+100/x)-37=0

We get rid of parentheses

x+100/x-37=0

We multiply all the terms by the denominator


x*x-37*x+100=0

We add all the numbers together, and all the variables

-37x+x*x+100=0

Wy multiply elements

x^2-37x+100=0

a = 1; b = -37; c = +100;
Δ = b2-4ac
Δ = -372-4·1·100
Δ = 969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-\sqrt{969}}{2*1}=\frac{37-\sqrt{969}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{969}}{2*1}=\frac{37+\sqrt{969}}{2}
$