x^2-12x+36=(16)^3

Solution for x^2-12x+36=(16)^3 equation:

x^2-12x+36=(16)^3

We move all terms to the left:

x^2-12x+36-((16)^3)=0

determiningTheFunctionDomain
x^2-12x+36-16^3=0

We add all the numbers together, and all the variables

x^2-12x-4060=0

a = 1; b = -12; c = -4060;
Δ = b2-4ac
Δ = -122-4·1·(-4060)
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-128}{2*1}=\frac{-116}{2}
=-58
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+128}{2*1}=\frac{140}{2}
=70
$