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5n^2+51n+54=0
a = 5; b = 51; c = +54;
Δ = b2-4ac
Δ = 512-4·5·54
Δ = 1521
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{1521}=39$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-39}{2*5}=\frac{-90}{10} =-9 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+39}{2*5}=\frac{-12}{10} =-1+1/5 $
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