1/3a-1=5/12a+2

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Solution for 1/3a-1=5/12a+2 equation:



1/3a-1=5/12a+2
We move all terms to the left:
1/3a-1-(5/12a+2)=0
Domain of the equation: 3a!=0
a!=0/3
a!=0
a∈R
Domain of the equation: 12a+2)!=0
a∈R
We get rid of parentheses
1/3a-5/12a-2-1=0
We calculate fractions
12a/36a^2+(-15a)/36a^2-2-1=0
We add all the numbers together, and all the variables
12a/36a^2+(-15a)/36a^2-3=0
We multiply all the terms by the denominator
12a+(-15a)-3*36a^2=0
Wy multiply elements
-108a^2+12a+(-15a)=0
We get rid of parentheses
-108a^2+12a-15a=0
We add all the numbers together, and all the variables
-108a^2-3a=0
a = -108; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-108)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-108}=\frac{0}{-216} =0 $
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-108}=\frac{6}{-216} =-1/36 $

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