2/8a-3=1/3a+6

Solution for 2/8a-3=1/3a+6 equation:

2/8a-3=1/3a+6

We move all terms to the left:

2/8a-3-(1/3a+6)=0


Domain of the equation: 8a!=0

a!=0/8

a!=0

a∈R



Domain of the equation: 3a+6)!=0

a∈R


We get rid of parentheses

2/8a-1/3a-6-3=0

We calculate fractions


6a/24a^2+(-8a)/24a^2-6-3=0

We add all the numbers together, and all the variables

6a/24a^2+(-8a)/24a^2-9=0

We multiply all the terms by the denominator


6a+(-8a)-9*24a^2=0

Wy multiply elements

-216a^2+6a+(-8a)=0

We get rid of parentheses

-216a^2+6a-8a=0

We add all the numbers together, and all the variables

-216a^2-2a=0

a = -216; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-216)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-216}=\frac{0}{-432}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-216}=\frac{4}{-432}
=-1/108
$