b^2-9b-54=0

Solution for b^2-9b-54=0 equation:

b^2-9b-54=0

a = 1; b = -9; c = -54;
Δ = b2-4ac
Δ = -92-4·1·(-54)
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{33}}{2*1}=\frac{9-3\sqrt{33}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{33}}{2*1}=\frac{9+3\sqrt{33}}{2}
$