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

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
$