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7n^2-5n-78=0
a = 7; b = -5; c = -78;
Δ = b2-4ac
Δ = -52-4·7·(-78)
Δ = 2209
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{2209}=47$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-47}{2*7}=\frac{-42}{14} =-3 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+47}{2*7}=\frac{52}{14} =3+5/7 $
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