0=6x^2+84x+288

Solution for 0=6x^2+84x+288 equation:

0=6x^2+84x+288

We move all terms to the left:

0-(6x^2+84x+288)=0

We add all the numbers together, and all the variables

-(6x^2+84x+288)=0

We get rid of parentheses

-6x^2-84x-288=0

a = -6; b = -84; c = -288;
Δ = b2-4ac
Δ = -842-4·(-6)·(-288)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-12}{2*-6}=\frac{72}{-12}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+12}{2*-6}=\frac{96}{-12}
=-8
$