8n(2n-+7)=11

Solution for 8n(2n-+7)=11 equation:

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}
$