F(x)=4-3x/x

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

(F)=4-3F/F

We move all terms to the left:

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


Domain of the equation: F)!=0

F!=0/1

F!=0

F∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

F+3F/F-4=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-1F+F*F=0

Wy multiply elements

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