F(x)=24/3x-2

Solution for F(x)=24/3x-2 equation:

(F)=24/3F-2

We move all terms to the left:

(F)-(24/3F-2)=0


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

F∈R


We get rid of parentheses

F-24/3F+2=0

We multiply all the terms by the denominator


F*3F+2*3F-24=0

Wy multiply elements

3F^2+6F-24=0

a = 3; b = 6; c = -24;
Δ = b2-4ac
Δ = 62-4·3·(-24)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-18}{2*3}=\frac{-24}{6}
=-4
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+18}{2*3}=\frac{12}{6}
=2
$