9(b^2-24)=0

Solution for 9(b^2-24)=0 equation:

9(b^2-24)=0

We multiply parentheses

9b^2-216=0

a = 9; b = 0; c = -216;
Δ = b2-4ac
Δ = 02-4·9·(-216)
Δ = 7776
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:

$\sqrt{\Delta}=\sqrt{7776}=\sqrt{1296*6}=\sqrt{1296}*\sqrt{6}=36\sqrt{6}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{6}}{2*9}=\frac{0-36\sqrt{6}}{18}
=-\frac{36\sqrt{6}}{18}
=-2\sqrt{6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{6}}{2*9}=\frac{0+36\sqrt{6}}{18}
=\frac{36\sqrt{6}}{18}
=2\sqrt{6}
$