F(x)=1/6x-3

Solution for F(x)=1/6x-3 equation:

(F)=1/6F-3

We move all terms to the left:

(F)-(1/6F-3)=0


Domain of the equation: 6F-3)!=0

F∈R


We get rid of parentheses

F-1/6F+3=0

We multiply all the terms by the denominator


F*6F+3*6F-1=0

Wy multiply elements

6F^2+18F-1=0

a = 6; b = 18; c = -1;
Δ = b2-4ac
Δ = 182-4·6·(-1)
Δ = 348
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:

$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{87}}{2*6}=\frac{-18-2\sqrt{87}}{12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{87}}{2*6}=\frac{-18+2\sqrt{87}}{12}
$