9a(3-a)=11

Solution for 9a(3-a)=11 equation:

9a(3-a)=11

We move all terms to the left:

9a(3-a)-(11)=0

We add all the numbers together, and all the variables

9a(-1a+3)-11=0

We multiply parentheses

-9a^2+27a-11=0

a = -9; b = 27; c = -11;
Δ = b2-4ac
Δ = 272-4·(-9)·(-11)
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{37}}{2*-9}=\frac{-27-3\sqrt{37}}{-18}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{37}}{2*-9}=\frac{-27+3\sqrt{37}}{-18}
$