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42n^2-217n+280=0
a = 42; b = -217; c = +280;
Δ = b2-4ac
Δ = -2172-4·42·280
Δ = 49
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{49}=7$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-217)-7}{2*42}=\frac{210}{84} =2+1/2 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-217)+7}{2*42}=\frac{224}{84} =2+2/3 $
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