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5N^2-58N-24=0
a = 5; b = -58; c = -24;
Δ = b2-4ac
Δ = -582-4·5·(-24)
Δ = 3844
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{3844}=62$$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-62}{2*5}=\frac{-4}{10} =-2/5 $$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+62}{2*5}=\frac{120}{10} =12 $
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