1/x+x=140

Solution for 1/x+x=140 equation:

1/x+x=140

We move all terms to the left:

1/x+x-(140)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+1/x-140=0

We multiply all the terms by the denominator


x*x-140*x+1=0

We add all the numbers together, and all the variables

-140x+x*x+1=0

Wy multiply elements

x^2-140x+1=0

a = 1; b = -140; c = +1;
Δ = b2-4ac
Δ = -1402-4·1·1
Δ = 19596
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:

$\sqrt{\Delta}=\sqrt{19596}=\sqrt{4*4899}=\sqrt{4}*\sqrt{4899}=2\sqrt{4899}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-2\sqrt{4899}}{2*1}=\frac{140-2\sqrt{4899}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+2\sqrt{4899}}{2*1}=\frac{140+2\sqrt{4899}}{2}
$