2/9a+2/3a=7

Solution for 2/9a+2/3a=7 equation:

2/9a+2/3a=7

We move all terms to the left:

2/9a+2/3a-(7)=0


Domain of the equation: 9a!=0

a!=0/9

a!=0

a∈R



Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We calculate fractions


6a/27a^2+18a/27a^2-7=0

We multiply all the terms by the denominator


6a+18a-7*27a^2=0

We add all the numbers together, and all the variables

24a-7*27a^2=0

Wy multiply elements

-189a^2+24a=0

a = -189; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-189)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-189}=\frac{-48}{-378}
=8/63
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-189}=\frac{0}{-378}
=0
$