F(x)=2/3x-2

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

(F)=2/3F-2

We move all terms to the left:

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


Domain of the equation: 3F-2)!=0

F∈R


We get rid of parentheses

F-2/3F+2=0

We multiply all the terms by the denominator


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

Wy multiply elements

3F^2+6F-2=0

a = 3; b = 6; c = -2;
Δ = b2-4ac
Δ = 62-4·3·(-2)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{15}}{2*3}=\frac{-6-2\sqrt{15}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{15}}{2*3}=\frac{-6+2\sqrt{15}}{6}
$