5/8a+6=3/9a

Solution for 5/8a+6=3/9a equation:

5/8a+6=3/9a

We move all terms to the left:

5/8a+6-(3/9a)=0


Domain of the equation: 8a!=0

a!=0/8

a!=0

a∈R



Domain of the equation: 9a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

5/8a-(+3/9a)+6=0

We get rid of parentheses

5/8a-3/9a+6=0

We calculate fractions


45a/72a^2+(-24a)/72a^2+6=0

We multiply all the terms by the denominator


45a+(-24a)+6*72a^2=0

Wy multiply elements

432a^2+45a+(-24a)=0

We get rid of parentheses

432a^2+45a-24a=0

We add all the numbers together, and all the variables

432a^2+21a=0

a = 432; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·432·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*432}=\frac{-42}{864}
=-7/144
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*432}=\frac{0}{864}
=0
$