(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-3)!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

-1x+(3x+2)-(4x/x-3)=0

We get rid of parentheses

-1x+3x-4x/x+2+3=0

We multiply all the terms by the denominator


-1x*x+3x*x-4x+2*x+3*x=0

We add all the numbers together, and all the variables

x-1x*x+3x*x=0

Wy multiply elements

-1x^2+3x^2+x=0

We add all the numbers together, and all the variables

2x^2+x=0

a = 2; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·2·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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