12x+(-x^2)=12

Solution for 12x+(-x^2)=12 equation:

12x+(-x^2)=12

We move all terms to the left:

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

We get rid of parentheses

-x^2+12x-12=0

We add all the numbers together, and all the variables

-1x^2+12x-12=0

a = -1; b = 12; c = -12;
Δ = b2-4ac
Δ = 122-4·(-1)·(-12)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{6}}{2*-1}=\frac{-12-4\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{6}}{2*-1}=\frac{-12+4\sqrt{6}}{-2}
$