1/3a-4(2/3a-3)=2/3a-6

Solution for 1/3a-4(2/3a-3)=2/3a-6 equation:

1/3a-4(2/3a-3)=2/3a-6

We move all terms to the left:

1/3a-4(2/3a-3)-(2/3a-6)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 3a-3)!=0

a∈R



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

a∈R


We multiply parentheses

1/3a-8a-(2/3a-6)+12=0

We get rid of parentheses

1/3a-8a-2/3a+6+12=0

We multiply all the terms by the denominator


-8a*3a+6*3a+12*3a+1-2=0

We add all the numbers together, and all the variables

-8a*3a+6*3a+12*3a-1=0

Wy multiply elements

-24a^2+18a+36a-1=0

We add all the numbers together, and all the variables

-24a^2+54a-1=0

a = -24; b = 54; c = -1;
Δ = b2-4ac
Δ = 542-4·(-24)·(-1)
Δ = 2820
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2820}=\sqrt{4*705}=\sqrt{4}*\sqrt{705}=2\sqrt{705}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{705}}{2*-24}=\frac{-54-2\sqrt{705}}{-48}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{705}}{2*-24}=\frac{-54+2\sqrt{705}}{-48}
$