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2(3x-6)(4x+9)=0
We multiply parentheses ..
2(+12x^2+27x-24x-54)=0
We multiply parentheses
24x^2+54x-48x-108=0
We add all the numbers together, and all the variables
24x^2+6x-108=0
a = 24; b = 6; c = -108;
Δ = b2-4ac
Δ = 62-4·24·(-108)
Δ = 10404
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{10404}=102$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-102}{2*24}=\frac{-108}{48} =-2+1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+102}{2*24}=\frac{96}{48} =2 $
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