3/a+4=3/2a

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

3/a+4=3/2a

We move all terms to the left:

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


Domain of the equation: a!=0

a∈R



Domain of the equation: 2a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

8a^2+6a-3a=0

We add all the numbers together, and all the variables

8a^2+3a=0

a = 8; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·8·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*8}=\frac{-6}{16}
=-3/8
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*8}=\frac{0}{16}
=0
$