2/5a-5+8/9a=19

Solution for 2/5a-5+8/9a=19 equation:

2/5a-5+8/9a=19

We move all terms to the left:

2/5a-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

2/5a+8/9a-24=0

We calculate fractions


18a/45a^2+40a/45a^2-24=0

We multiply all the terms by the denominator


18a+40a-24*45a^2=0

We add all the numbers together, and all the variables

58a-24*45a^2=0

Wy multiply elements

-1080a^2+58a=0

a = -1080; b = 58; c = 0;
Δ = b2-4ac
Δ = 582-4·(-1080)·0
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-58}{2*-1080}=\frac{-116}{-2160}
=29/540
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+58}{2*-1080}=\frac{0}{-2160}
=0
$