x^2-4x+4=5.25

Solution for x^2-4x+4=5.25 equation:

x^2-4x+4=5.25

We move all terms to the left:

x^2-4x+4-(5.25)=0

We add all the numbers together, and all the variables

x^2-4x-1.25=0

a = 1; b = -4; c = -1.25;
Δ = b2-4ac
Δ = -42-4·1·(-1.25)
Δ = 21
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{21}}{2*1}=\frac{4-\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+\sqrt{21}}{2*1}=\frac{4+\sqrt{21}}{2}
$