F(x)=6/x-2

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

(F)=6/F-2

We move all terms to the left:

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


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

F∈R


We get rid of parentheses

F-6/F+2=0

We multiply all the terms by the denominator


F*F+2*F-6=0

We add all the numbers together, and all the variables

2F+F*F-6=0

Wy multiply elements

F^2+2F-6=0

a = 1; b = 2; c = -6;
Δ = b2-4ac
Δ = 22-4·1·(-6)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{7}}{2*1}=\frac{-2-2\sqrt{7}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{7}}{2*1}=\frac{-2+2\sqrt{7}}{2}
$