F(x)=9/3x-18

Solution for F(x)=9/3x-18 equation:

(F)=9/3F-18

We move all terms to the left:

(F)-(9/3F-18)=0


Domain of the equation: 3F-18)!=0

F∈R


We get rid of parentheses

F-9/3F+18=0

We multiply all the terms by the denominator


F*3F+18*3F-9=0

Wy multiply elements

3F^2+54F-9=0

a = 3; b = 54; c = -9;
Δ = b2-4ac
Δ = 542-4·3·(-9)
Δ = 3024
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:

$\sqrt{\Delta}=\sqrt{3024}=\sqrt{144*21}=\sqrt{144}*\sqrt{21}=12\sqrt{21}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-12\sqrt{21}}{2*3}=\frac{-54-12\sqrt{21}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+12\sqrt{21}}{2*3}=\frac{-54+12\sqrt{21}}{6}
$