4/3a-17-5/9a=11

Solution for 4/3a-17-5/9a=11 equation:

4/3a-17-5/9a=11

We move all terms to the left:

4/3a-17-5/9a-(11)=0


Domain of the equation: 3a!=0

a!=0/3

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

4/3a-5/9a-28=0

We calculate fractions


36a/27a^2+(-15a)/27a^2-28=0

We multiply all the terms by the denominator


36a+(-15a)-28*27a^2=0

Wy multiply elements

-756a^2+36a+(-15a)=0

We get rid of parentheses

-756a^2+36a-15a=0

We add all the numbers together, and all the variables

-756a^2+21a=0

a = -756; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-756)·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*-756}=\frac{-42}{-1512}
=1/36
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-756}=\frac{0}{-1512}
=0
$