x=3-1/x

Solution for x=3-1/x equation:

x=3-1/x

We move all terms to the left:

x-(3-1/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+3)=0

We get rid of parentheses

x+1/x-3=0

We multiply all the terms by the denominator


x*x-3*x+1=0

We add all the numbers together, and all the variables

-3x+x*x+1=0

Wy multiply elements

x^2-3x+1=0

a = 1; b = -3; c = +1;
Δ = b2-4ac
Δ = -32-4·1·1
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{-(-3)-\sqrt{5}}{2*1}=\frac{3-\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{5}}{2*1}=\frac{3+\sqrt{5}}{2}
$