a^2-4a+4=81

Solution for a^2-4a+4=81 equation:

a^2-4a+4=81

We move all terms to the left:

a^2-4a+4-(81)=0

We add all the numbers together, and all the variables

a^2-4a-77=0

a = 1; b = -4; c = -77;
Δ = b2-4ac
Δ = -42-4·1·(-77)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-18}{2*1}=\frac{-14}{2}
=-7
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+18}{2*1}=\frac{22}{2}
=11
$