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

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

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

We move all terms to the left:

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


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 6a+8)!=0

a∈R


We get rid of parentheses

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

We calculate fractions


12a/18a^2+(-3a)/18a^2-8+1=0

We add all the numbers together, and all the variables

12a/18a^2+(-3a)/18a^2-7=0

We multiply all the terms by the denominator


12a+(-3a)-7*18a^2=0

Wy multiply elements

-126a^2+12a+(-3a)=0

We get rid of parentheses

-126a^2+12a-3a=0

We add all the numbers together, and all the variables

-126a^2+9a=0

a = -126; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-126)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-126}=\frac{-18}{-252}
=1/14
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-126}=\frac{0}{-252}
=0
$