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4n^2-7n-65=0
a = 4; b = -7; c = -65;
Δ = b2-4ac
Δ = -72-4·4·(-65)
Δ = 1089
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{1089}=33$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-33}{2*4}=\frac{-26}{8} =-3+1/4 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+33}{2*4}=\frac{40}{8} =5 $
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