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3x(x-4)+21(x-4)=0
We multiply parentheses
3x^2-12x+21x-84=0
We add all the numbers together, and all the variables
3x^2+9x-84=0
a = 3; b = 9; c = -84;
Δ = b2-4ac
Δ = 92-4·3·(-84)
Δ = 1089
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{1089}=33$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-33}{2*3}=\frac{-42}{6} =-7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+33}{2*3}=\frac{24}{6} =4 $
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