9b^2-9b-23=0

Solution for 9b^2-9b-23=0 equation:

9b^2-9b-23=0

a = 9; b = -9; c = -23;
Δ = b2-4ac
Δ = -92-4·9·(-23)
Δ = 909
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:

$\sqrt{\Delta}=\sqrt{909}=\sqrt{9*101}=\sqrt{9}*\sqrt{101}=3\sqrt{101}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{101}}{2*9}=\frac{9-3\sqrt{101}}{18}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{101}}{2*9}=\frac{9+3\sqrt{101}}{18}
$