4/3a-1/12a+13/6=8/3

Solution for 4/3a-1/12a+13/6=8/3 equation:

4/3a-1/12a+13/6=8/3

We move all terms to the left:

4/3a-1/12a+13/6-(8/3)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 12a!=0

a!=0/12

a!=0

a∈R


We add all the numbers together, and all the variables

4/3a-1/12a+13/6-(+8/3)=0

We get rid of parentheses

4/3a-1/12a+13/6-8/3=0

We calculate fractions


1404a^2/3888a^2+1728a/3888a^2+(-324a)/3888a^2+(-3456a)/3888a^2=0

We multiply all the terms by the denominator


1404a^2+1728a+(-324a)+(-3456a)=0

We get rid of parentheses

1404a^2+1728a-324a-3456a=0

We add all the numbers together, and all the variables

1404a^2-2052a=0

a = 1404; b = -2052; c = 0;
Δ = b2-4ac
Δ = -20522-4·1404·0
Δ = 4210704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4210704}=2052$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2052)-2052}{2*1404}=\frac{0}{2808}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2052)+2052}{2*1404}=\frac{4104}{2808}
=1+6/13
$