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1-(2x-x^2)=0.1
We move all terms to the left:
1-(2x-x^2)-(0.1)=0
We add all the numbers together, and all the variables
-(2x-x^2)+0.9=0
We get rid of parentheses
x^2-2x+0.9=0
a = 1; b = -2; c = +0.9;
Δ = b2-4ac
Δ = -22-4·1·0.9
Δ = 0.4
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{0.4}}{2*1}=\frac{2-\sqrt{0.4}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{0.4}}{2*1}=\frac{2+\sqrt{0.4}}{2} $
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