2x-4/3x-9=3x

Solution for 2x-4/3x-9=3x equation:

2x-4/3x-9=3x

We move all terms to the left:

2x-4/3x-9-(3x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-1x-4/3x-9=0

We multiply all the terms by the denominator


-1x*3x-9*3x-4=0

Wy multiply elements

-3x^2-27x-4=0

a = -3; b = -27; c = -4;
Δ = b2-4ac
Δ = -272-4·(-3)·(-4)
Δ = 681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{681}}{2*-3}=\frac{27-\sqrt{681}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{681}}{2*-3}=\frac{27+\sqrt{681}}{-6}
$