a/3a+2=a-16*

Solution for a/3a+2=a-16* equation:

a/3a+2=a-16*

We move all terms to the left:

a/3a+2-(a-16*)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

a/3a-a+2=0

We multiply all the terms by the denominator


a-a*3a+2*3a=0

Wy multiply elements

-3a^2+a+6a=0

We add all the numbers together, and all the variables

-3a^2+7a=0

a = -3; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-3)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-3}=\frac{-14}{-6}
=2+1/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-3}=\frac{0}{-6}
=0
$