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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

3x/6x^2+(-2x)/6x^2-7=0

We multiply all the terms by the denominator


3x+(-2x)-7*6x^2=0

Wy multiply elements

-42x^2+3x+(-2x)=0

We get rid of parentheses

-42x^2+3x-2x=0

We add all the numbers together, and all the variables

-42x^2+x=0

a = -42; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-42)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-42}=\frac{-2}{-84}
=1/42
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-42}=\frac{0}{-84}
=0
$