F(x)=6-9x/2x

Solution for F(x)=6-9x/2x equation:

(F)=6-9F/2F

We move all terms to the left:

(F)-(6-9F/2F)=0


Domain of the equation: 2F)!=0

F!=0/1

F!=0

F∈R


We add all the numbers together, and all the variables

F-(-9F/2F+6)=0

We get rid of parentheses

F+9F/2F-6=0

We multiply all the terms by the denominator


F*2F+9F-6*2F=0

We add all the numbers together, and all the variables

9F+F*2F-6*2F=0

Wy multiply elements

2F^2+9F-12F=0

We add all the numbers together, and all the variables

2F^2-3F=0

a = 2; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·2·0
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*2}=\frac{0}{4}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*2}=\frac{6}{4}
=1+1/2
$