F(x)=3x+9/3x-7

Solution for F(x)=3x+9/3x-7 equation:

(F)=3F+9/3F-7

We move all terms to the left:

(F)-(3F+9/3F-7)=0


Domain of the equation: 3F-7)!=0

F∈R


We get rid of parentheses

F-3F-9/3F+7=0

We multiply all the terms by the denominator


F*3F-3F*3F+7*3F-9=0

Wy multiply elements

3F^2-9F^2+21F-9=0

We add all the numbers together, and all the variables

-6F^2+21F-9=0

a = -6; b = 21; c = -9;
Δ = b2-4ac
Δ = 212-4·(-6)·(-9)
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{-(21)-15}{2*-6}=\frac{-36}{-12}
=+3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+15}{2*-6}=\frac{-6}{-12}
=1/2
$