F(x)=3x-6/x-2

Solution for F(x)=3x-6/x-2 equation:

(F)=3F-6/F-2

We move all terms to the left:

(F)-(3F-6/F-2)=0


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

F∈R


We get rid of parentheses

F-3F+6/F+2=0

We multiply all the terms by the denominator


F*F-3F*F+2*F+6=0

We add all the numbers together, and all the variables

2F+F*F-3F*F+6=0

Wy multiply elements

F^2-3F^2+2F+6=0

We add all the numbers together, and all the variables

-2F^2+2F+6=0

a = -2; b = 2; c = +6;
Δ = b2-4ac
Δ = 22-4·(-2)·6
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{13}}{2*-2}=\frac{-2-2\sqrt{13}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{13}}{2*-2}=\frac{-2+2\sqrt{13}}{-4}
$