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12(x-4)(3x+2)=0
We multiply parentheses ..
12(+3x^2+2x-12x-8)=0
We multiply parentheses
36x^2+24x-144x-96=0
We add all the numbers together, and all the variables
36x^2-120x-96=0
a = 36; b = -120; c = -96;
Δ = b2-4ac
Δ = -1202-4·36·(-96)
Δ = 28224
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{28224}=168$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-168}{2*36}=\frac{-48}{72} =-2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+168}{2*36}=\frac{288}{72} =4 $
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