F(x)=1/6x-18

Solution for F(x)=1/6x-18 equation:

(F)=1/6F-18

We move all terms to the left:

(F)-(1/6F-18)=0


Domain of the equation: 6F-18)!=0

F∈R


We get rid of parentheses

F-1/6F+18=0

We multiply all the terms by the denominator


F*6F+18*6F-1=0

Wy multiply elements

6F^2+108F-1=0

a = 6; b = 108; c = -1;
Δ = b2-4ac
Δ = 1082-4·6·(-1)
Δ = 11688
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:

$\sqrt{\Delta}=\sqrt{11688}=\sqrt{4*2922}=\sqrt{4}*\sqrt{2922}=2\sqrt{2922}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-2\sqrt{2922}}{2*6}=\frac{-108-2\sqrt{2922}}{12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+2\sqrt{2922}}{2*6}=\frac{-108+2\sqrt{2922}}{12}
$