3/5a-5+8/9a=-19

Solution for 3/5a-5+8/9a=-19 equation:

3/5a-5+8/9a=-19

We move all terms to the left:

3/5a-5+8/9a-(-19)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R



Domain of the equation: 9a!=0

a!=0/9

a!=0

a∈R


We add all the numbers together, and all the variables

3/5a+8/9a+14=0

We calculate fractions


27a/45a^2+40a/45a^2+14=0

We multiply all the terms by the denominator


27a+40a+14*45a^2=0

We add all the numbers together, and all the variables

67a+14*45a^2=0

Wy multiply elements

630a^2+67a=0

a = 630; b = 67; c = 0;
Δ = b2-4ac
Δ = 672-4·630·0
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(67)-67}{2*630}=\frac{-134}{1260}
=-67/630
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(67)+67}{2*630}=\frac{0}{1260}
=0
$