3a(3a+3)+6=81

Solution for 3a(3a+3)+6=81 equation:

3a(3a+3)+6=81

We move all terms to the left:

3a(3a+3)+6-(81)=0

We add all the numbers together, and all the variables

3a(3a+3)-75=0

We multiply parentheses

9a^2+9a-75=0

a = 9; b = 9; c = -75;
Δ = b2-4ac
Δ = 92-4·9·(-75)
Δ = 2781
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:

$\sqrt{\Delta}=\sqrt{2781}=\sqrt{9*309}=\sqrt{9}*\sqrt{309}=3\sqrt{309}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{309}}{2*9}=\frac{-9-3\sqrt{309}}{18}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{309}}{2*9}=\frac{-9+3\sqrt{309}}{18}
$