0=3x^2+33x+54

Solution for 0=3x^2+33x+54 equation:

0=3x^2+33x+54

We move all terms to the left:

0-(3x^2+33x+54)=0

We add all the numbers together, and all the variables

-(3x^2+33x+54)=0

We get rid of parentheses

-3x^2-33x-54=0

a = -3; b = -33; c = -54;
Δ = b2-4ac
Δ = -332-4·(-3)·(-54)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-21}{2*-3}=\frac{12}{-6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+21}{2*-3}=\frac{54}{-6}
=-9
$