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7n^2+46n-80=0
a = 7; b = 46; c = -80;
Δ = b2-4ac
Δ = 462-4·7·(-80)
Δ = 4356
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{4356}=66$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-66}{2*7}=\frac{-112}{14} =-8 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+66}{2*7}=\frac{20}{14} =1+3/7 $
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