2a/a+6=3a+2

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

2a/a+6=3a+2

We move all terms to the left:

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


Domain of the equation: a!=0

a∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

6a-3a*a=0

Wy multiply elements

-3a^2+6a=0

a = -3; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-3)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-3}=\frac{-12}{-6}
=+2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-3}=\frac{0}{-6}
=0
$