x^2=12x+32=0

Solution for x^2=12x+32=0 equation:

x^2=12x+32=0

We move all terms to the left:

x^2-(12x+32)=0

We get rid of parentheses

x^2-12x-32=0

a = 1; b = -12; c = -32;
Δ = b2-4ac
Δ = -122-4·1·(-32)
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{17}}{2*1}=\frac{12-4\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{17}}{2*1}=\frac{12+4\sqrt{17}}{2}
$