7/6x+1/3x=2+5/3x

Solution for 7/6x+1/3x=2+5/3x equation:

7/6x+1/3x=2+5/3x

We move all terms to the left:

7/6x+1/3x-(2+5/3x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

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

7/6x+1/3x-(5/3x+2)=0

We get rid of parentheses

7/6x+1/3x-5/3x-2=0

We calculate fractions


21x/18x^2+(-30x+1)/18x^2-2=0

We multiply all the terms by the denominator


21x+(-30x+1)-2*18x^2=0

Wy multiply elements

-36x^2+21x+(-30x+1)=0

We get rid of parentheses

-36x^2+21x-30x+1=0

We add all the numbers together, and all the variables

-36x^2-9x+1=0

a = -36; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·(-36)·1
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-15}{2*-36}=\frac{-6}{-72}
=1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15}{2*-36}=\frac{24}{-72}
=-1/3
$