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6n^2+30n=84
We move all terms to the left:
6n^2+30n-(84)=0
a = 6; b = 30; c = -84;
Δ = b2-4ac
Δ = 302-4·6·(-84)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{2916}=54$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-54}{2*6}=\frac{-84}{12} =-7 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+54}{2*6}=\frac{24}{12} =2 $
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