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

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

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

We move all terms to the left:

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


Domain of the equation: 3F(3-1))!=0

F∈R


We add all the numbers together, and all the variables

-(1/3F2)+3=0

We get rid of parentheses

-1/3F2+3=0

We multiply all the terms by the denominator


3*3F2-1=0

Wy multiply elements

9F^2-1=0

a = 9; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·9·(-1)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*9}=\frac{-6}{18}
=-1/3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*9}=\frac{6}{18}
=1/3
$