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

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

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

We move all terms to the left:

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


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



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

a∈R


We get rid of parentheses

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

We calculate fractions


9a/6a^2+(-8a)/6a^2-4+1=0

We add all the numbers together, and all the variables

9a/6a^2+(-8a)/6a^2-3=0

We multiply all the terms by the denominator


9a+(-8a)-3*6a^2=0

Wy multiply elements

-18a^2+9a+(-8a)=0

We get rid of parentheses

-18a^2+9a-8a=0

We add all the numbers together, and all the variables

-18a^2+a=0

a = -18; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-18)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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