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

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

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

We move all terms to the left:

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


Domain of the equation: 3(a+2)!=0

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


2a/(6a+12)+(-3aa/(6a+12)=0


We calculate terms in parentheses: +(-3aa/(6a+12), so:

-3aa/(6a+12

We multiply all the terms by the denominator


-3aa

Back to the equation:

+(-3aa)


We get rid of parentheses

2a/(6a+12)-3aa=0

We multiply all the terms by the denominator


2a-3aa*(6a+12)=0

We multiply parentheses

-18a^2+2a-36a=0

We add all the numbers together, and all the variables

-18a^2-34a=0

a = -18; b = -34; c = 0;
Δ = b2-4ac
Δ = -342-4·(-18)·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-34}{2*-18}=\frac{0}{-36}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+34}{2*-18}=\frac{68}{-36}
=-1+8/9
$