x+2=1/x

Solution for x+2=1/x equation:

x+2=1/x

We move all terms to the left:

x+2-(1/x)=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-(+1/x)+2=0

We get rid of parentheses

x-1/x+2=0

We multiply all the terms by the denominator


x*x+2*x-1=0

We add all the numbers together, and all the variables

2x+x*x-1=0

Wy multiply elements

x^2+2x-1=0

a = 1; b = 2; c = -1;
Δ = b2-4ac
Δ = 22-4·1·(-1)
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{2}}{2*1}=\frac{-2-2\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{2}}{2*1}=\frac{-2+2\sqrt{2}}{2}
$