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x^2-2x+1=0.5
We move all terms to the left:
x^2-2x+1-(0.5)=0
We add all the numbers together, and all the variables
x^2-2x+0.5=0
a = 1; b = -2; c = +0.5;
Δ = b2-4ac
Δ = -22-4·1·0.5
Δ = 2
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{-(-2)-\sqrt{2}}{2*1}=\frac{2-\sqrt{2}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{2}}{2*1}=\frac{2+\sqrt{2}}{2} $
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