2/3*a+2=1/3*4a+1

Solution for 2/3*a+2=1/3*4a+1 equation:

2/3a+2=1/3*4a+1

We move all terms to the left:

2/3a+2-(1/3*4a+1)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 3*4a+1)!=0

a∈R


We get rid of parentheses

2/3a-1/3*4a-1+2=0

We calculate fractions


96a/144a^2+(-3a)/144a^2-1+2=0

We add all the numbers together, and all the variables

96a/144a^2+(-3a)/144a^2+1=0

We multiply all the terms by the denominator


96a+(-3a)+1*144a^2=0

Wy multiply elements

144a^2+96a+(-3a)=0

We get rid of parentheses

144a^2+96a-3a=0

We add all the numbers together, and all the variables

144a^2+93a=0

a = 144; b = 93; c = 0;
Δ = b2-4ac
Δ = 932-4·144·0
Δ = 8649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8649}=93$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(93)-93}{2*144}=\frac{-186}{288}
=-31/48
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(93)+93}{2*144}=\frac{0}{288}
=0
$