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

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

(F)=3F/F-4F

We move all terms to the left:

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


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

F∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

F+4F-3F/F=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

5F^2-3F=0

a = 5; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·5·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*5}=\frac{0}{10}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*5}=\frac{6}{10}
=3/5
$