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

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

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

We move all terms to the left:

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


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 2a+3)!=0

a∈R


We get rid of parentheses

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

We calculate fractions


2a/6a^2+(-9a)/6a^2-3+4=0

We add all the numbers together, and all the variables

2a/6a^2+(-9a)/6a^2+1=0

We multiply all the terms by the denominator


2a+(-9a)+1*6a^2=0

Wy multiply elements

6a^2+2a+(-9a)=0

We get rid of parentheses

6a^2+2a-9a=0

We add all the numbers together, and all the variables

6a^2-7a=0

a = 6; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·6·0
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*6}=\frac{0}{12}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*6}=\frac{14}{12}
=1+1/6
$