8b^2-6b-1=0

Solution for 8b^2-6b-1=0 equation:

8b^2-6b-1=0

a = 8; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·8·(-1)
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{17}}{2*8}=\frac{6-2\sqrt{17}}{16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{17}}{2*8}=\frac{6+2\sqrt{17}}{16}
$