F(x)=3/x+2

Solution for F(x)=3/x+2 equation:

(F)=3/F+2

We move all terms to the left:

(F)-(3/F+2)=0


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

F∈R


We get rid of parentheses

F-3/F-2=0

We multiply all the terms by the denominator


F*F-2*F-3=0

We add all the numbers together, and all the variables

-2F+F*F-3=0

Wy multiply elements

F^2-2F-3=0

a = 1; b = -2; c = -3;
Δ = b2-4ac
Δ = -22-4·1·(-3)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4}{2*1}=\frac{-2}{2}
=-1
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4}{2*1}=\frac{6}{2}
=3
$