2x+7/3x-9=x

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

2x+7/3x-9=x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+7/3x-9=0

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2-27x+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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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