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

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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 $

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