F(x)=9x/6x-11

Solution for F(x)=9x/6x-11 equation:

(F)=9F/6F-11

We move all terms to the left:

(F)-(9F/6F-11)=0


Domain of the equation: 6F-11)!=0

F∈R


We get rid of parentheses

F-9F/6F+11=0

We multiply all the terms by the denominator


F*6F-9F+11*6F=0

We add all the numbers together, and all the variables

-9F+F*6F+11*6F=0

Wy multiply elements

6F^2-9F+66F=0

We add all the numbers together, and all the variables

6F^2+57F=0

a = 6; b = 57; c = 0;
Δ = b2-4ac
Δ = 572-4·6·0
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-57}{2*6}=\frac{-114}{12}
=-9+1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+57}{2*6}=\frac{0}{12}
=0
$