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5n^2-31n-2=0
a = 5; b = -31; c = -2;
Δ = b2-4ac
Δ = -312-4·5·(-2)
Δ = 1001
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-\sqrt{1001}}{2*5}=\frac{31-\sqrt{1001}}{10} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{1001}}{2*5}=\frac{31+\sqrt{1001}}{10} $
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