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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-12x^2)/216x^2+144x/216x^2+(-324x)/216x^2-1=0

We multiply all the terms by the denominator


(-12x^2)+144x+(-324x)-1*216x^2=0

Wy multiply elements

(-12x^2)-216x^2+144x+(-324x)=0

We get rid of parentheses

-12x^2-216x^2+144x-324x=0

We add all the numbers together, and all the variables

-228x^2-180x=0

a = -228; b = -180; c = 0;
Δ = b2-4ac
Δ = -1802-4·(-228)·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-180}{2*-228}=\frac{0}{-456}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+180}{2*-228}=\frac{360}{-456}
=-15/19
$