1/3a+9(a+4)=0

Solution for 1/3a+9(a+4)=0 equation:

1/3a+9(a+4)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We multiply parentheses

1/3a+9a+36=0

We multiply all the terms by the denominator


9a*3a+36*3a+1=0

Wy multiply elements

27a^2+108a+1=0

a = 27; b = 108; c = +1;
Δ = b2-4ac
Δ = 1082-4·27·1
Δ = 11556
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:

$\sqrt{\Delta}=\sqrt{11556}=\sqrt{36*321}=\sqrt{36}*\sqrt{321}=6\sqrt{321}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-6\sqrt{321}}{2*27}=\frac{-108-6\sqrt{321}}{54}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+6\sqrt{321}}{2*27}=\frac{-108+6\sqrt{321}}{54}
$