X2-2x+1=45

Solution for X2-2x+1=45 equation:

X2-2X+1=45

We move all terms to the left:

X2-2X+1-(45)=0

We add all the numbers together, and all the variables

X^2-2X-44=0

a = 1; b = -2; c = -44;
Δ = b2-4ac
Δ = -22-4·1·(-44)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{5}}{2*1}=\frac{2-6\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{5}}{2*1}=\frac{2+6\sqrt{5}}{2}
$