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4n^2-14n-800=0
a = 4; b = -14; c = -800;
Δ = b2-4ac
Δ = -142-4·4·(-800)
Δ = 12996
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{12996}=114$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-114}{2*4}=\frac{-100}{8} =-12+1/2 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+114}{2*4}=\frac{128}{8} =16 $
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