0=27-12x-x^2

Solution for 0=27-12x-x^2 equation:

0=27-12x-x^2

We move all terms to the left:

0-(27-12x-x^2)=0

We add all the numbers together, and all the variables

-(27-12x-x^2)=0

We get rid of parentheses

x^2+12x-27=0

a = 1; b = 12; c = -27;
Δ = b2-4ac
Δ = 122-4·1·(-27)
Δ = 252
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{7}}{2*1}=\frac{-12-6\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{7}}{2*1}=\frac{-12+6\sqrt{7}}{2}
$