F(x)=1/6x-2

Solution for F(x)=1/6x-2 equation:

(F)=1/6F-2

We move all terms to the left:

(F)-(1/6F-2)=0


Domain of the equation: 6F-2)!=0

F∈R


We get rid of parentheses

F-1/6F+2=0

We multiply all the terms by the denominator


F*6F+2*6F-1=0

Wy multiply elements

6F^2+12F-1=0

a = 6; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·6·(-1)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{42}}{2*6}=\frac{-12-2\sqrt{42}}{12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{42}}{2*6}=\frac{-12+2\sqrt{42}}{12}
$