F(n)=1/3n+8

Solution for F(n)=1/3n+8 equation:

(F)=1/3F+8

We move all terms to the left:

(F)-(1/3F+8)=0


Domain of the equation: 3F+8)!=0

F∈R


We get rid of parentheses

F-1/3F-8=0

We multiply all the terms by the denominator


F*3F-8*3F-1=0

Wy multiply elements

3F^2-24F-1=0

a = 3; b = -24; c = -1;
Δ = b2-4ac
Δ = -242-4·3·(-1)
Δ = 588
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:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-14\sqrt{3}}{2*3}=\frac{24-14\sqrt{3}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+14\sqrt{3}}{2*3}=\frac{24+14\sqrt{3}}{6}
$