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6(x-2)(x-9)=0
We multiply parentheses ..
6(+x^2-9x-2x+18)=0
We multiply parentheses
6x^2-54x-12x+108=0
We add all the numbers together, and all the variables
6x^2-66x+108=0
a = 6; b = -66; c = +108;
Δ = b2-4ac
Δ = -662-4·6·108
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-42}{2*6}=\frac{24}{12} =2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+42}{2*6}=\frac{108}{12} =9 $
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