F(x)=4-3/3x

Solution for F(x)=4-3/3x equation:

(F)=4-3/3F

We move all terms to the left:

(F)-(4-3/3F)=0


Domain of the equation: 3F)!=0

F!=0/1

F!=0

F∈R


We add all the numbers together, and all the variables

F-(-3/3F+4)=0

We get rid of parentheses

F+3/3F-4=0

We multiply all the terms by the denominator


F*3F-4*3F+3=0

Wy multiply elements

3F^2-12F+3=0

a = 3; b = -12; c = +3;
Δ = b2-4ac
Δ = -122-4·3·3
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{3}}{2*3}=\frac{12-6\sqrt{3}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{3}}{2*3}=\frac{12+6\sqrt{3}}{6}
$