X^2-12x+32=4

Solution for X^2-12x+32=4 equation:

X^2-12X+32=4

We move all terms to the left:

X^2-12X+32-(4)=0

We add all the numbers together, and all the variables

X^2-12X+28=0

a = 1; b = -12; c = +28;
Δ = b2-4ac
Δ = -122-4·1·28
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{2}}{2*1}=\frac{12-4\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{2}}{2*1}=\frac{12+4\sqrt{2}}{2}
$