12=36x+x^2

Solution for 12=36x+x^2 equation:

12=36x+x^2

We move all terms to the left:

12-(36x+x^2)=0

We get rid of parentheses

-x^2-36x+12=0

We add all the numbers together, and all the variables

-1x^2-36x+12=0

a = -1; b = -36; c = +12;
Δ = b2-4ac
Δ = -362-4·(-1)·12
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-8\sqrt{21}}{2*-1}=\frac{36-8\sqrt{21}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+8\sqrt{21}}{2*-1}=\frac{36+8\sqrt{21}}{-2}
$