1/6x-3=3/2x

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

1/6x-3=3/2x

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


2x/12x^2+(-18x)/12x^2-3=0

We multiply all the terms by the denominator


2x+(-18x)-3*12x^2=0

Wy multiply elements

-36x^2+2x+(-18x)=0

We get rid of parentheses

-36x^2+2x-18x=0

We add all the numbers together, and all the variables

-36x^2-16x=0

a = -36; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-36)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-36}=\frac{0}{-72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-36}=\frac{32}{-72}
=-4/9
$