-3(2+a)=1/3a+(-3)

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

-3(2+a)=1/3a+(-3)

We move all terms to the left:

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


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

a∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We multiply all the terms by the denominator


-3a*3a-6*3a+(-3))-(1+(-3))=0

We add all the numbers together, and all the variables

-3a*3a-6*3a=0

Wy multiply elements

-9a^2-18a=0

a = -9; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-9)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-9}=\frac{0}{-18}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-9}=\frac{36}{-18}
=-2
$