1/2x-2/3=4/6x+2

Solution for 1/2x-2/3=4/6x+2 equation:

1/2x-2/3=4/6x+2

We move all terms to the left:

1/2x-2/3-(4/6x+2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

1/2x-4/6x-2-2/3=0

We calculate fractions


(-144x^2)/108x^2+54x/108x^2+(-72x)/108x^2-2=0

We multiply all the terms by the denominator


(-144x^2)+54x+(-72x)-2*108x^2=0

Wy multiply elements

(-144x^2)-216x^2+54x+(-72x)=0

We get rid of parentheses

-144x^2-216x^2+54x-72x=0

We add all the numbers together, and all the variables

-360x^2-18x=0

a = -360; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-360)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-360}=\frac{0}{-720}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-360}=\frac{36}{-720}
=-1/20
$