1/2a-1/3a=4

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Solution for 1/2a-1/3a=4 equation:



1/2a-1/3a=4
We move all terms to the left:
1/2a-1/3a-(4)=0
Domain of the equation: 2a!=0
a!=0/2
a!=0
a∈R
Domain of the equation: 3a!=0
a!=0/3
a!=0
a∈R
We calculate fractions
3a/6a^2+(-2a)/6a^2-4=0
We multiply all the terms by the denominator
3a+(-2a)-4*6a^2=0
Wy multiply elements
-24a^2+3a+(-2a)=0
We get rid of parentheses
-24a^2+3a-2a=0
We add all the numbers together, and all the variables
-24a^2+a=0
a = -24; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-24)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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

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