2/3a-2=5/6a

Solution for 2/3a-2=5/6a equation:

2/3a-2=5/6a

We move all terms to the left:

2/3a-2-(5/6a)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 6a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

2/3a-(+5/6a)-2=0

We get rid of parentheses

2/3a-5/6a-2=0

We calculate fractions


12a/18a^2+(-15a)/18a^2-2=0

We multiply all the terms by the denominator


12a+(-15a)-2*18a^2=0

Wy multiply elements

-36a^2+12a+(-15a)=0

We get rid of parentheses

-36a^2+12a-15a=0

We add all the numbers together, and all the variables

-36a^2-3a=0

a = -36; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-36)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-36}=\frac{0}{-72}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-36}=\frac{6}{-72}
=-1/12
$