(6)(1/3)(4a+1)=(6)(1/2)(a)

Solution for (6)(1/3)(4a+1)=(6)(1/2)(a) equation:

(6)(1/3)(4a+1)=(6)(1/2)(a)

We move all terms to the left:

(6)(1/3)(4a+1)-((6)(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

6(+1/3)(4a+1)-(6(+1/2)a)=0

We multiply parentheses ..

6(+4a^2+1/3*1)-(6(+1/2)a)=0

We calculate fractions


(24a^2+12a)/6a^2+()/6a^2=0

We multiply all the terms by the denominator


(24a^2+12a)+()=0

We add all the numbers together, and all the variables

(24a^2+12a)=0

We get rid of parentheses

24a^2+12a=0

a = 24; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·24·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*24}=\frac{-24}{48}
=-1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*24}=\frac{0}{48}
=0
$