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2(x+6)(3x-9)=0
We multiply parentheses ..
2(+3x^2-9x+18x-54)=0
We multiply parentheses
6x^2-18x+36x-108=0
We add all the numbers together, and all the variables
6x^2+18x-108=0
a = 6; b = 18; c = -108;
Δ = b2-4ac
Δ = 182-4·6·(-108)
Δ = 2916
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{2916}=54$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-54}{2*6}=\frac{-72}{12} =-6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+54}{2*6}=\frac{36}{12} =3 $
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