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n(8n-7)=8481
We move all terms to the left:
n(8n-7)-(8481)=0
We multiply parentheses
8n^2-7n-8481=0
a = 8; b = -7; c = -8481;
Δ = b2-4ac
Δ = -72-4·8·(-8481)
Δ = 271441
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{271441}=521$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-521}{2*8}=\frac{-514}{16} =-32+1/8 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+521}{2*8}=\frac{528}{16} =33 $
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