x^2-4x+4=75

Solution for x^2-4x+4=75 equation:

x^2-4x+4=75

We move all terms to the left:

x^2-4x+4-(75)=0

We add all the numbers together, and all the variables

x^2-4x-71=0

a = 1; b = -4; c = -71;
Δ = b2-4ac
Δ = -42-4·1·(-71)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-10\sqrt{3}}{2*1}=\frac{4-10\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+10\sqrt{3}}{2*1}=\frac{4+10\sqrt{3}}{2}
$