8b^2-18b-9=0

Solution for 8b^2-18b-9=0 equation:

8b^2-18b-9=0

a = 8; b = -18; c = -9;
Δ = b2-4ac
Δ = -182-4·8·(-9)
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{17}}{2*8}=\frac{18-6\sqrt{17}}{16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{17}}{2*8}=\frac{18+6\sqrt{17}}{16}
$