3/4a-1/6=2/3a

Solution for 3/4a-1/6=2/3a equation:

3/4a-1/6=2/3a

We move all terms to the left:

3/4a-1/6-(2/3a)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 3a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

3/4a-(+2/3a)-1/6=0

We get rid of parentheses

3/4a-2/3a-1/6=0

We calculate fractions


(-36a^2)/432a^2+324a/432a^2+(-288a)/432a^2=0

We multiply all the terms by the denominator


(-36a^2)+324a+(-288a)=0

We get rid of parentheses

-36a^2+324a-288a=0

We add all the numbers together, and all the variables

-36a^2+36a=0

a = -36; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-36)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-36}=\frac{-72}{-72}
=1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-36}=\frac{0}{-72}
=0
$