2-2/3x=5/6x+8

Solution for 2-2/3x=5/6x+8 equation:

2-2/3x=5/6x+8

We move all terms to the left:

2-2/3x-(5/6x+8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x+8)!=0

x∈R


We get rid of parentheses

-2/3x-5/6x-8+2=0

We calculate fractions


(-12x)/18x^2+(-15x)/18x^2-8+2=0

We add all the numbers together, and all the variables

(-12x)/18x^2+(-15x)/18x^2-6=0

We multiply all the terms by the denominator


(-12x)+(-15x)-6*18x^2=0

Wy multiply elements

-108x^2+(-12x)+(-15x)=0

We get rid of parentheses

-108x^2-12x-15x=0

We add all the numbers together, and all the variables

-108x^2-27x=0

a = -108; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·(-108)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*-108}=\frac{0}{-216}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*-108}=\frac{54}{-216}
=-1/4
$