1/x+1=x

Solution for 1/x+1=x equation:

1/x+1=x

We move all terms to the left:

1/x+1-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+1/x+1=0

We multiply all the terms by the denominator


-1x*x+1*x+1=0

We add all the numbers together, and all the variables

x-1x*x+1=0

Wy multiply elements

-1x^2+x+1=0

a = -1; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-1)·1
Δ = 5
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{-(1)-\sqrt{5}}{2*-1}=\frac{-1-\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{5}}{2*-1}=\frac{-1+\sqrt{5}}{-2}
$