F(x)=1/x+1

Solution for F(x)=1/x+1 equation:

(F)=1/F+1

We move all terms to the left:

(F)-(1/F+1)=0


Domain of the equation: F+1)!=0

F∈R


We get rid of parentheses

F-1/F-1=0

We multiply all the terms by the denominator


F*F-1*F-1=0

We add all the numbers together, and all the variables

-1F+F*F-1=0

Wy multiply elements

F^2-1F-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:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{5}}{2*1}=\frac{1-\sqrt{5}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{5}}{2*1}=\frac{1+\sqrt{5}}{2}
$