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

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

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

We move all terms to the left:

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


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 3a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3/2a-2/3a+5/6=0

We calculate fractions


90a^2/216a^2+324a/216a^2+(-144a)/216a^2=0

We multiply all the terms by the denominator


90a^2+324a+(-144a)=0

We get rid of parentheses

90a^2+324a-144a=0

We add all the numbers together, and all the variables

90a^2+180a=0

a = 90; b = 180; c = 0;
Δ = b2-4ac
Δ = 1802-4·90·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-180}{2*90}=\frac{-360}{180}
=-2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+180}{2*90}=\frac{0}{180}
=0
$