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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


144x^2/108x^2+(-54x)/108x^2+90x/108x^2-1=0

We multiply all the terms by the denominator


144x^2+(-54x)+90x-1*108x^2=0

We add all the numbers together, and all the variables

144x^2+90x+(-54x)-1*108x^2=0

Wy multiply elements

144x^2-108x^2+90x+(-54x)=0

We get rid of parentheses

144x^2-108x^2+90x-54x=0

We add all the numbers together, and all the variables

36x^2+36x=0

a = 36; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·36·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*36}=\frac{-72}{72}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*36}=\frac{0}{72}
=0
$