5/8a=6+4/9a

Solution for 5/8a=6+4/9a equation:

5/8a=6+4/9a

We move all terms to the left:

5/8a-(6+4/9a)=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-(4/9a+6)=0

We get rid of parentheses

5/8a-4/9a-6=0

We calculate fractions


45a/72a^2+(-32a)/72a^2-6=0

We multiply all the terms by the denominator


45a+(-32a)-6*72a^2=0

Wy multiply elements

-432a^2+45a+(-32a)=0

We get rid of parentheses

-432a^2+45a-32a=0

We add all the numbers together, and all the variables

-432a^2+13a=0

a = -432; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-432)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-432}=\frac{-26}{-864}
=13/432
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-432}=\frac{0}{-864}
=0
$