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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


108x^2/72x^2+(-48x)/72x^2+(-60x)/72x^2+2=0

We multiply all the terms by the denominator


108x^2+(-48x)+(-60x)+2*72x^2=0

Wy multiply elements

108x^2+144x^2+(-48x)+(-60x)=0

We get rid of parentheses

108x^2+144x^2-48x-60x=0

We add all the numbers together, and all the variables

252x^2-108x=0

a = 252; b = -108; c = 0;
Δ = b2-4ac
Δ = -1082-4·252·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-108}{2*252}=\frac{0}{504}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+108}{2*252}=\frac{216}{504}
=3/7
$