F(x)=2/3x-4

Solution for F(x)=2/3x-4 equation:

(F)=2/3F-4

We move all terms to the left:

(F)-(2/3F-4)=0


Domain of the equation: 3F-4)!=0

F∈R


We get rid of parentheses

F-2/3F+4=0

We multiply all the terms by the denominator


F*3F+4*3F-2=0

Wy multiply elements

3F^2+12F-2=0

a = 3; b = 12; c = -2;
Δ = b2-4ac
Δ = 122-4·3·(-2)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{42}}{2*3}=\frac{-12-2\sqrt{42}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{42}}{2*3}=\frac{-12+2\sqrt{42}}{6}
$