F(x)=1/3x-6

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

(F)=1/3F-6

We move all terms to the left:

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


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

F∈R


We get rid of parentheses

F-1/3F+6=0

We multiply all the terms by the denominator


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

Wy multiply elements

3F^2+18F-1=0

a = 3; b = 18; c = -1;
Δ = b2-4ac
Δ = 182-4·3·(-1)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-4\sqrt{21}}{2*3}=\frac{-18-4\sqrt{21}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+4\sqrt{21}}{2*3}=\frac{-18+4\sqrt{21}}{6}
$