F(x)=1/6x+8

Solution for F(x)=1/6x+8 equation:

(F)=1/6F+8

We move all terms to the left:

(F)-(1/6F+8)=0


Domain of the equation: 6F+8)!=0

F∈R


We get rid of parentheses

F-1/6F-8=0

We multiply all the terms by the denominator


F*6F-8*6F-1=0

Wy multiply elements

6F^2-48F-1=0

a = 6; b = -48; c = -1;
Δ = b2-4ac
Δ = -482-4·6·(-1)
Δ = 2328
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:

$\sqrt{\Delta}=\sqrt{2328}=\sqrt{4*582}=\sqrt{4}*\sqrt{582}=2\sqrt{582}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{582}}{2*6}=\frac{48-2\sqrt{582}}{12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{582}}{2*6}=\frac{48+2\sqrt{582}}{12}
$