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3x(x+9)=11
We move all terms to the left:
3x(x+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 = 861
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{861}}{2*3}=\frac{-27-\sqrt{861}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{861}}{2*3}=\frac{-27+\sqrt{861}}{6} $
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