3x(-x-9)=11

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

3x(-x-9)=11

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x(-1x-9)-11=0

We multiply parentheses

-3x^2-27x-11=0

a = -3; b = -27; c = -11;
Δ = b2-4ac
Δ = -272-4·(-3)·(-11)
Δ = 597
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{597}}{2*-3}=\frac{27-\sqrt{597}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{597}}{2*-3}=\frac{27+\sqrt{597}}{-6}
$