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

1/x-(x+1)=0

We get rid of parentheses

1/x-x-1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-1x-x*x+1=0

Wy multiply elements

-1x^2-1x+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}
$