X^2-2x+5=12

Solution for X^2-2x+5=12 equation:

X^2-2X+5=12

We move all terms to the left:

X^2-2X+5-(12)=0

We add all the numbers together, and all the variables

X^2-2X-7=0

a = 1; b = -2; c = -7;
Δ = b2-4ac
Δ = -22-4·1·(-7)
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{-(-2)-4\sqrt{2}}{2*1}=\frac{2-4\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{2}}{2*1}=\frac{2+4\sqrt{2}}{2}
$