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3(3x-4)(2x-7)=0
We multiply parentheses ..
3(+6x^2-21x-8x+28)=0
We multiply parentheses
18x^2-63x-24x+84=0
We add all the numbers together, and all the variables
18x^2-87x+84=0
a = 18; b = -87; c = +84;
Δ = b2-4ac
Δ = -872-4·18·84
Δ = 1521
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{1521}=39$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-87)-39}{2*18}=\frac{48}{36} =1+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-87)+39}{2*18}=\frac{126}{36} =3+1/2 $
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