5/9a-3=3a+5

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

5/9a-3=3a+5

We move all terms to the left:

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


Domain of the equation: 9a!=0

a!=0/9

a!=0

a∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-3a*9a-5*9a-3*9a+5=0

Wy multiply elements

-27a^2-45a-27a+5=0

We add all the numbers together, and all the variables

-27a^2-72a+5=0

a = -27; b = -72; c = +5;
Δ = b2-4ac
Δ = -722-4·(-27)·5
Δ = 5724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5724}=\sqrt{36*159}=\sqrt{36}*\sqrt{159}=6\sqrt{159}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-6\sqrt{159}}{2*-27}=\frac{72-6\sqrt{159}}{-54}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+6\sqrt{159}}{2*-27}=\frac{72+6\sqrt{159}}{-54}
$