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8n(2n+7)=35
We move all terms to the left:
8n(2n+7)-(35)=0
We multiply parentheses
16n^2+56n-35=0
a = 16; b = 56; c = -35;
Δ = b2-4ac
Δ = 562-4·16·(-35)
Δ = 5376
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5376}=\sqrt{256*21}=\sqrt{256}*\sqrt{21}=16\sqrt{21}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-16\sqrt{21}}{2*16}=\frac{-56-16\sqrt{21}}{32} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+16\sqrt{21}}{2*16}=\frac{-56+16\sqrt{21}}{32} $
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