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500n^2+2700n-77000=0
a = 500; b = 2700; c = -77000;
Δ = b2-4ac
Δ = 27002-4·500·(-77000)
Δ = 161290000
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{161290000}=12700$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2700)-12700}{2*500}=\frac{-15400}{1000} =-15+2/5 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2700)+12700}{2*500}=\frac{10000}{1000} =10 $
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