5/3a-2+6/2=3/2a-4

Solution for 5/3a-2+6/2=3/2a-4 equation:

5/3a-2+6/2=3/2a-4

We move all terms to the left:

5/3a-2+6/2-(3/2a-4)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 2a-4)!=0

a∈R


We add all the numbers together, and all the variables

5/3a-(3/2a-4)+1=0

We get rid of parentheses

5/3a-3/2a+4+1=0

We calculate fractions


10a/6a^2+(-9a)/6a^2+4+1=0

We add all the numbers together, and all the variables

10a/6a^2+(-9a)/6a^2+5=0

We multiply all the terms by the denominator


10a+(-9a)+5*6a^2=0

Wy multiply elements

30a^2+10a+(-9a)=0

We get rid of parentheses

30a^2+10a-9a=0

We add all the numbers together, and all the variables

30a^2+a=0

a = 30; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·30·0
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*30}=\frac{-2}{60}
=-1/30
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*30}=\frac{0}{60}
=0
$