1/6x+3=1/2x

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

1/6x+3=1/2x

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


2x/12x^2+(-6x)/12x^2+3=0

We multiply all the terms by the denominator


2x+(-6x)+3*12x^2=0

Wy multiply elements

36x^2+2x+(-6x)=0

We get rid of parentheses

36x^2+2x-6x=0

We add all the numbers together, and all the variables

36x^2-4x=0

a = 36; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·36·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*36}=\frac{0}{72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*36}=\frac{8}{72}
=1/9
$