0=6x2+54x+120

Solution for 0=6x2+54x+120 equation:

0=6x^2+54x+120

We move all terms to the left:

0-(6x^2+54x+120)=0

We add all the numbers together, and all the variables

-(6x^2+54x+120)=0

We get rid of parentheses

-6x^2-54x-120=0

a = -6; b = -54; c = -120;
Δ = b2-4ac
Δ = -542-4·(-6)·(-120)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6}{2*-6}=\frac{48}{-12}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6}{2*-6}=\frac{60}{-12}
=-5
$