8b^2-8b-5=0

Solution for 8b^2-8b-5=0 equation:

8b^2-8b-5=0

a = 8; b = -8; c = -5;
Δ = b2-4ac
Δ = -82-4·8·(-5)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{14}}{2*8}=\frac{8-4\sqrt{14}}{16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{14}}{2*8}=\frac{8+4\sqrt{14}}{16}
$