144=36x-x^2

Solution for 144=36x-x^2 equation:

144=36x-x^2

We move all terms to the left:

144-(36x-x^2)=0

We get rid of parentheses

x^2-36x+144=0

a = 1; b = -36; c = +144;
Δ = b2-4ac
Δ = -362-4·1·144
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{-(-36)-12\sqrt{5}}{2*1}=\frac{36-12\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{5}}{2*1}=\frac{36+12\sqrt{5}}{2}
$