8b^2-11=-8b

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

8b^2-11=-8b

We move all terms to the left:

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

We get rid of parentheses

8b^2+8b-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:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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