x^2-4x+4=9.5

Solution for x^2-4x+4=9.5 equation:

x^2-4x+4=9.5

We move all terms to the left:

x^2-4x+4-(9.5)=0

We add all the numbers together, and all the variables

x^2-4x-5.5=0

a = 1; b = -4; c = -5.5;
Δ = b2-4ac
Δ = -42-4·1·(-5.5)
Δ = 38
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-\sqrt{38}}{2*1}=\frac{4-\sqrt{38}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+\sqrt{38}}{2*1}=\frac{4+\sqrt{38}}{2}
$