5/6x=6/3x+2

Solution for 5/6x=6/3x+2 equation:

5/6x=6/3x+2

We move all terms to the left:

5/6x-(6/3x+2)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x+2)!=0

x∈R


We get rid of parentheses

5/6x-6/3x-2=0

We calculate fractions


15x/18x^2+(-36x)/18x^2-2=0

We multiply all the terms by the denominator


15x+(-36x)-2*18x^2=0

Wy multiply elements

-36x^2+15x+(-36x)=0

We get rid of parentheses

-36x^2+15x-36x=0

We add all the numbers together, and all the variables

-36x^2-21x=0

a = -36; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·(-36)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*-36}=\frac{0}{-72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*-36}=\frac{42}{-72}
=-7/12
$