F(x)=3(x-2/3)+2

Solution for F(x)=3(x-2/3)+2 equation:

(F)=3(F-2/3)+2

We move all terms to the left:

(F)-(3(F-2/3)+2)=0

We add all the numbers together, and all the variables

F-(3(+F-2/3)+2)=0

We multiply all the terms by the denominator


F*3)+2)-(3(+F-2=0

We add all the numbers together, and all the variables

F+F*3)+2)-(3(-2=0

Wy multiply elements

3F^2+F-2=0

a = 3; b = 1; c = -2;
Δ = b2-4ac
Δ = 12-4·3·(-2)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5}{2*3}=\frac{-6}{6}
=-1
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5}{2*3}=\frac{4}{6}
=2/3
$