3b^2=9b+54

Solution for 3b^2=9b+54 equation:

3b^2=9b+54

We move all terms to the left:

3b^2-(9b+54)=0

We get rid of parentheses

3b^2-9b-54=0

a = 3; b = -9; c = -54;
Δ = b2-4ac
Δ = -92-4·3·(-54)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-27}{2*3}=\frac{-18}{6}
=-3
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+27}{2*3}=\frac{36}{6}
=6
$