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

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

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

We move all terms to the left:

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


Domain of the equation: a!=0

a∈R



Domain of the equation: 2a+1)!=0

a∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


4a+(-3a)-4*2a^2=0

Wy multiply elements

-8a^2+4a+(-3a)=0

We get rid of parentheses

-8a^2+4a-3a=0

We add all the numbers together, and all the variables

-8a^2+a=0

a = -8; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-8)·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*-8}=\frac{-2}{-16}
=1/8
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-8}=\frac{0}{-16}
=0
$