3x-6/3-4x/x-3=x

Solution for 3x-6/3-4x/x-3=x equation:

3x-6/3-4x/x-3=x

We move all terms to the left:

3x-6/3-4x/x-3-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x-4x/x-5=0

We multiply all the terms by the denominator


2x*x-4x-5*x=0

We add all the numbers together, and all the variables

-9x+2x*x=0

Wy multiply elements

2x^2-9x=0

a = 2; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·2·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*2}=\frac{18}{4}
=4+1/2
$