F(x)=6-3x/x-4

Solution for F(x)=6-3x/x-4 equation:

(F)=6-3F/F-4

We move all terms to the left:

(F)-(6-3F/F-4)=0


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

F∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

F+3F/F-2=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

F+F*F=0

Wy multiply elements

F^2+F=0

a = 1; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·1·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*1}=\frac{-2}{2}
=-1
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*1}=\frac{0}{2}
=0
$