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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+5-6)!=0

We move all terms containing x to the left, all other terms to the right

2x-6)!=-5

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-12x^2)/216x^2+144x/216x^2+(-108x)/216x^2+1=0

We multiply all the terms by the denominator


(-12x^2)+144x+(-108x)+1*216x^2=0

Wy multiply elements

(-12x^2)+216x^2+144x+(-108x)=0

We get rid of parentheses

-12x^2+216x^2+144x-108x=0

We add all the numbers together, and all the variables

204x^2+36x=0

a = 204; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·204·0
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*204}=\frac{-72}{408}
=-3/17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*204}=\frac{0}{408}
=0
$