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8n(6n+1)=392
We move all terms to the left:
8n(6n+1)-(392)=0
We multiply parentheses
48n^2+8n-392=0
a = 48; b = 8; c = -392;
Δ = b2-4ac
Δ = 82-4·48·(-392)
Δ = 75328
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{75328}=\sqrt{64*1177}=\sqrt{64}*\sqrt{1177}=8\sqrt{1177}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{1177}}{2*48}=\frac{-8-8\sqrt{1177}}{96} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{1177}}{2*48}=\frac{-8+8\sqrt{1177}}{96} $
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