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(2x-4)(6x+9)=0
We multiply parentheses ..
(+12x^2+18x-24x-36)=0
We get rid of parentheses
12x^2+18x-24x-36=0
We add all the numbers together, and all the variables
12x^2-6x-36=0
a = 12; b = -6; c = -36;
Δ = b2-4ac
Δ = -62-4·12·(-36)
Δ = 1764
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{1764}=42$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-42}{2*12}=\frac{-36}{24} =-1+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+42}{2*12}=\frac{48}{24} =2 $
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