F(x)=2/3x-1

Solution for F(x)=2/3x-1 equation:

(F)=2/3F-1

We move all terms to the left:

(F)-(2/3F-1)=0


Domain of the equation: 3F-1)!=0

F∈R


We get rid of parentheses

F-2/3F+1=0

We multiply all the terms by the denominator


F*3F+1*3F-2=0

Wy multiply elements

3F^2+3F-2=0

a = 3; b = 3; c = -2;
Δ = b2-4ac
Δ = 32-4·3·(-2)
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{33}}{2*3}=\frac{-3-\sqrt{33}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{33}}{2*3}=\frac{-3+\sqrt{33}}{6}
$