x2-6x+9=256

Solution for x2-6x+9=256 equation:

x2-6x+9=256

We move all terms to the left:

x2-6x+9-(256)=0

We add all the numbers together, and all the variables

x^2-6x-247=0

a = 1; b = -6; c = -247;
Δ = b2-4ac
Δ = -62-4·1·(-247)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-32}{2*1}=\frac{-26}{2}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+32}{2*1}=\frac{38}{2}
=19
$