a*3-11a^2-9a=-99

Solution for a*3-11a^2-9a=-99 equation:

a*3-11a^2-9a=-99

We move all terms to the left:

a*3-11a^2-9a-(-99)=0

We add all the numbers together, and all the variables

-11a^2-9a+a*3+99=0

Wy multiply elements

-11a^2-9a+3a+99=0

We add all the numbers together, and all the variables

-11a^2-6a+99=0

a = -11; b = -6; c = +99;
Δ = b2-4ac
Δ = -62-4·(-11)·99
Δ = 4392
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:

$\sqrt{\Delta}=\sqrt{4392}=\sqrt{36*122}=\sqrt{36}*\sqrt{122}=6\sqrt{122}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{122}}{2*-11}=\frac{6-6\sqrt{122}}{-22}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{122}}{2*-11}=\frac{6+6\sqrt{122}}{-22}
$