F(x)=1/x+2

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

(F)=1/F+2

We move all terms to the left:

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


Domain of the equation: F+2)!=0

F∈R


We get rid of parentheses

F-1/F-2=0

We multiply all the terms by the denominator


F*F-2*F-1=0

We add all the numbers together, and all the variables

-2F+F*F-1=0

Wy multiply elements

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

The end solution:

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