2/3a+1/a=3

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

2/3a+1/a=3

We move all terms to the left:

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


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: a!=0

a∈R


We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

5a-3*3a^2=0

Wy multiply elements

-9a^2+5a=0

a = -9; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-9)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-9}=\frac{-10}{-18}
=5/9
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-9}=\frac{0}{-18}
=0
$