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8n^2+5n-62=0
a = 8; b = 5; c = -62;
Δ = b2-4ac
Δ = 52-4·8·(-62)
Δ = 2009
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2009}=\sqrt{49*41}=\sqrt{49}*\sqrt{41}=7\sqrt{41}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-7\sqrt{41}}{2*8}=\frac{-5-7\sqrt{41}}{16} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7\sqrt{41}}{2*8}=\frac{-5+7\sqrt{41}}{16} $
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