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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} $
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