F(x)=2/x+1

Solution for F(x)=2/x+1 equation:

(F)=2/F+1

We move all terms to the left:

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


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

F∈R


We get rid of parentheses

F-2/F-1=0

We multiply all the terms by the denominator


F*F-1*F-2=0

We add all the numbers together, and all the variables

-1F+F*F-2=0

Wy multiply elements

F^2-1F-2=0

a = 1; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·1·(-2)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3}{2*1}=\frac{-2}{2}
=-1
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3}{2*1}=\frac{4}{2}
=2
$