-8n^2=-11-8n

Solution for -8n^2=-11-8n equation:

-8n^2=-11-8n

We move all terms to the left:

-8n^2-(-11-8n)=0

We add all the numbers together, and all the variables

-8n^2-(-8n-11)=0

We get rid of parentheses

-8n^2+8n+11=0

a = -8; b = 8; c = +11;
Δ = b2-4ac
Δ = 82-4·(-8)·11
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{26}}{2*-8}=\frac{-8-4\sqrt{26}}{-16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{26}}{2*-8}=\frac{-8+4\sqrt{26}}{-16}
$