x^2-4x+4=289

Solution for x^2-4x+4=289 equation:

x^2-4x+4=289

We move all terms to the left:

x^2-4x+4-(289)=0

We add all the numbers together, and all the variables

x^2-4x-285=0

a = 1; b = -4; c = -285;
Δ = b2-4ac
Δ = -42-4·1·(-285)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-34}{2*1}=\frac{-30}{2}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+34}{2*1}=\frac{38}{2}
=19
$