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3(x-6)(2x-7)=0
We multiply parentheses ..
3(+2x^2-7x-12x+42)=0
We multiply parentheses
6x^2-21x-36x+126=0
We add all the numbers together, and all the variables
6x^2-57x+126=0
a = 6; b = -57; c = +126;
Δ = b2-4ac
Δ = -572-4·6·126
Δ = 225
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{225}=15$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-15}{2*6}=\frac{42}{12} =3+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+15}{2*6}=\frac{72}{12} =6 $
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