32=16x-x^2

Solution for 32=16x-x^2 equation:

32=16x-x^2

We move all terms to the left:

32-(16x-x^2)=0

We get rid of parentheses

x^2-16x+32=0

a = 1; b = -16; c = +32;
Δ = b2-4ac
Δ = -162-4·1·32
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{2}}{2*1}=\frac{16-8\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{2}}{2*1}=\frac{16+8\sqrt{2}}{2}
$