x^2-2x+4=67

Solution for x^2-2x+4=67 equation:

x^2-2x+4=67

We move all terms to the left:

x^2-2x+4-(67)=0

We add all the numbers together, and all the variables

x^2-2x-63=0

a = 1; b = -2; c = -63;
Δ = b2-4ac
Δ = -22-4·1·(-63)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-16}{2*1}=\frac{-14}{2}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+16}{2*1}=\frac{18}{2}
=9
$