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8n(2n-+7)=11
We move all terms to the left:
8n(2n-+7)-(11)=0
We add all the numbers together, and all the variables
8n(+2n)-11=0
We multiply parentheses
16n^2-11=0
a = 16; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·16·(-11)
Δ = 704
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{11}}{2*16}=\frac{0-8\sqrt{11}}{32} =-\frac{8\sqrt{11}}{32} =-\frac{\sqrt{11}}{4} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{11}}{2*16}=\frac{0+8\sqrt{11}}{32} =\frac{8\sqrt{11}}{32} =\frac{\sqrt{11}}{4} $
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