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6(x-4)(3x+8)=0
We multiply parentheses ..
6(+3x^2+8x-12x-32)=0
We multiply parentheses
18x^2+48x-72x-192=0
We add all the numbers together, and all the variables
18x^2-24x-192=0
a = 18; b = -24; c = -192;
Δ = b2-4ac
Δ = -242-4·18·(-192)
Δ = 14400
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{14400}=120$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-120}{2*18}=\frac{-96}{36} =-2+2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+120}{2*18}=\frac{144}{36} =4 $
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