b(b-4.5)=9

Solution for b(b-4.5)=9 equation:

b(b-4.5)=9

We move all terms to the left:

b(b-4.5)-(9)=0

We multiply parentheses

b^2-4.5b-9=0

a = 1; b = -4.5; c = -9;
Δ = b2-4ac
Δ = -4.52-4·1·(-9)
Δ = 56.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4.5)-\sqrt{56.25}}{2*1}=\frac{4.5-\sqrt{56.25}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4.5)+\sqrt{56.25}}{2*1}=\frac{4.5+\sqrt{56.25}}{2}
$