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

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

(F)=3F/4F+6

We move all terms to the left:

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


Domain of the equation: 4F+6)!=0

F∈R


We get rid of parentheses

F-3F/4F-6=0

We multiply all the terms by the denominator


F*4F-3F-6*4F=0

We add all the numbers together, and all the variables

-3F+F*4F-6*4F=0

Wy multiply elements

4F^2-3F-24F=0

We add all the numbers together, and all the variables

4F^2-27F=0

a = 4; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·4·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*4}=\frac{0}{8}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*4}=\frac{54}{8}
=6+3/4
$