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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

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

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

2x/6x^2+3x/6x^2+2=0

We multiply all the terms by the denominator


2x+3x+2*6x^2=0

We add all the numbers together, and all the variables

5x+2*6x^2=0

Wy multiply elements

12x^2+5x=0

a = 12; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·12·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*12}=\frac{-10}{24}
=-5/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*12}=\frac{0}{24}
=0
$