5/6x-4=2/3x+2

Solution for 5/6x-4=2/3x+2 equation:

5/6x-4=2/3x+2

We move all terms to the left:

5/6x-4-(2/3x+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-2/3x-2-4=0

We calculate fractions


15x/18x^2+(-12x)/18x^2-2-4=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-108x^2+3x=0

a = -108; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-108)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-108}=\frac{-6}{-216}
=1/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-108}=\frac{0}{-216}
=0
$