1/2a-2=1/3a-1

Solution for 1/2a-2=1/3a-1 equation:

1/2a-2=1/3a-1

We move all terms to the left:

1/2a-2-(1/3a-1)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 3a-1)!=0

a∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


3a+(-2a)-1*6a^2=0

Wy multiply elements

-6a^2+3a+(-2a)=0

We get rid of parentheses

-6a^2+3a-2a=0

We add all the numbers together, and all the variables

-6a^2+a=0

a = -6; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-6)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-6}=\frac{-2}{-12}
=1/6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-6}=\frac{0}{-12}
=0
$