0=x^2+27x+72

Solution for 0=x^2+27x+72 equation:

0=x^2+27x+72

We move all terms to the left:

0-(x^2+27x+72)=0

We add all the numbers together, and all the variables

-(x^2+27x+72)=0

We get rid of parentheses

-x^2-27x-72=0

We add all the numbers together, and all the variables

-1x^2-27x-72=0

a = -1; b = -27; c = -72;
Δ = b2-4ac
Δ = -272-4·(-1)·(-72)
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{-(-27)-21}{2*-1}=\frac{6}{-2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+21}{2*-1}=\frac{48}{-2}
=-24
$