F(x)=3/x-1

Solution for F(x)=3/x-1 equation:

(F)=3/F-1

We move all terms to the left:

(F)-(3/F-1)=0


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

F∈R


We get rid of parentheses

F-3/F+1=0

We multiply all the terms by the denominator


F*F+1*F-3=0

We add all the numbers together, and all the variables

F+F*F-3=0

Wy multiply elements

F^2+F-3=0

a = 1; b = 1; c = -3;
Δ = b2-4ac
Δ = 12-4·1·(-3)
Δ = 13
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{13}}{2*1}=\frac{-1-\sqrt{13}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{13}}{2*1}=\frac{-1+\sqrt{13}}{2}
$