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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


135x/162x^2+(-12x)/162x^2+6x/162x^2-1=0

We multiply all the terms by the denominator


135x+(-12x)+6x-1*162x^2=0

We add all the numbers together, and all the variables

141x+(-12x)-1*162x^2=0

Wy multiply elements

-162x^2+141x+(-12x)=0

We get rid of parentheses

-162x^2+141x-12x=0

We add all the numbers together, and all the variables

-162x^2+129x=0

a = -162; b = 129; c = 0;
Δ = b2-4ac
Δ = 1292-4·(-162)·0
Δ = 16641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16641}=129$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(129)-129}{2*-162}=\frac{-258}{-324}
=43/54
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(129)+129}{2*-162}=\frac{0}{-324}
=0
$