3+4/6x=6-1/3x

Solution for 3+4/6x=6-1/3x equation:

3+4/6x=6-1/3x

We move all terms to the left:

3+4/6x-(6-1/3x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4/6x-(-1/3x+6)+3=0

We get rid of parentheses

4/6x+1/3x-6+3=0

We calculate fractions


12x/18x^2+6x/18x^2-6+3=0

We add all the numbers together, and all the variables

12x/18x^2+6x/18x^2-3=0

We multiply all the terms by the denominator


12x+6x-3*18x^2=0

We add all the numbers together, and all the variables

18x-3*18x^2=0

Wy multiply elements

-54x^2+18x=0

a = -54; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-54)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-54}=\frac{-36}{-108}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-54}=\frac{0}{-108}
=0
$