(1/3)(4a+1)=((1/2)a)

Solution for (1/3)(4a+1)=((1/2)a) equation:

(1/3)(4a+1)=((1/2)a)

We move all terms to the left:

(1/3)(4a+1)-(((1/2)a))=0


Domain of the equation: 3)(4a+1)!=0

a∈R



Domain of the equation: 2)a))!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

(+1/3)(4a+1)-(((+1/2)a))=0

We multiply parentheses ..

(+4a^2+1/3*1)-(((+1/2)a))=0

We calculate fractions


(4a^2+2a)/6a^2+()/6a^2=0

We multiply all the terms by the denominator


(4a^2+2a)+()=0

We add all the numbers together, and all the variables

(4a^2+2a)=0

We get rid of parentheses

4a^2+2a=0

a = 4; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·4·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*4}=\frac{-4}{8}
=-1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*4}=\frac{0}{8}
=0
$