F(x)=3x/2x+6

Solution for F(x)=3x/2x+6 equation:

(F)=3F/2F+6

We move all terms to the left:

(F)-(3F/2F+6)=0


Domain of the equation: 2F+6)!=0

F∈R


We get rid of parentheses

F-3F/2F-6=0

We multiply all the terms by the denominator


F*2F-3F-6*2F=0

We add all the numbers together, and all the variables

-3F+F*2F-6*2F=0

Wy multiply elements

2F^2-3F-12F=0

We add all the numbers together, and all the variables

2F^2-15F=0

a = 2; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·2·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*2}=\frac{0}{4}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*2}=\frac{30}{4}
=7+1/2
$