2/3a+6/9a=4

Solution for 2/3a+6/9a=4 equation:

2/3a+6/9a=4

We move all terms to the left:

2/3a+6/9a-(4)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 9a!=0

a!=0/9

a!=0

a∈R


We calculate fractions


18a/27a^2+18a/27a^2-4=0

We multiply all the terms by the denominator


18a+18a-4*27a^2=0

We add all the numbers together, and all the variables

36a-4*27a^2=0

Wy multiply elements

-108a^2+36a=0

a = -108; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-108)·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*-108}=\frac{-72}{-216}
=1/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-108}=\frac{0}{-216}
=0
$