2/3a+1/2a=21

Solution for 2/3a+1/2a=21 equation:

2/3a+1/2a=21

We move all terms to the left:

2/3a+1/2a-(21)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We calculate fractions


4a/6a^2+3a/6a^2-21=0

We multiply all the terms by the denominator


4a+3a-21*6a^2=0

We add all the numbers together, and all the variables

7a-21*6a^2=0

Wy multiply elements

-126a^2+7a=0

a = -126; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-126)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-126}=\frac{-14}{-252}
=1/18
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-126}=\frac{0}{-252}
=0
$