4b(6b-54)=0

Solution for 4b(6b-54)=0 equation:

4b(6b-54)=0

We multiply parentheses

24b^2-216b=0

a = 24; b = -216; c = 0;
Δ = b2-4ac
Δ = -2162-4·24·0
Δ = 46656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{46656}=216$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-216}{2*24}=\frac{0}{48}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+216}{2*24}=\frac{432}{48}
=9
$