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8n^2+55n+42=0
a = 8; b = 55; c = +42;
Δ = b2-4ac
Δ = 552-4·8·42
Δ = 1681
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{1681}=41$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-41}{2*8}=\frac{-96}{16} =-6 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+41}{2*8}=\frac{-14}{16} =-7/8 $
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