144=12x+x^2

Solution for 144=12x+x^2 equation:

144=12x+x^2

We move all terms to the left:

144-(12x+x^2)=0

We get rid of parentheses

-x^2-12x+144=0

We add all the numbers together, and all the variables

-1x^2-12x+144=0

a = -1; b = -12; c = +144;
Δ = b2-4ac
Δ = -122-4·(-1)·144
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{5}}{2*-1}=\frac{12-12\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{5}}{2*-1}=\frac{12+12\sqrt{5}}{-2}
$