F(x)=2x+7/3x-9

Solution for F(x)=2x+7/3x-9 equation:

(F)=2F+7/3F-9

We move all terms to the left:

(F)-(2F+7/3F-9)=0


Domain of the equation: 3F-9)!=0

F∈R


We get rid of parentheses

F-2F-7/3F+9=0

We multiply all the terms by the denominator


F*3F-2F*3F+9*3F-7=0

Wy multiply elements

3F^2-6F^2+27F-7=0

We add all the numbers together, and all the variables

-3F^2+27F-7=0

a = -3; b = 27; c = -7;
Δ = b2-4ac
Δ = 272-4·(-3)·(-7)
Δ = 645
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-\sqrt{645}}{2*-3}=\frac{-27-\sqrt{645}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{645}}{2*-3}=\frac{-27+\sqrt{645}}{-6}
$