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5x^2-5x=-1
We move all terms to the left:
5x^2-5x-(-1)=0
We add all the numbers together, and all the variables
5x^2-5x+1=0
a = 5; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·5·1
Δ = 5
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{-(-5)-\sqrt{5}}{2*5}=\frac{5-\sqrt{5}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{5}}{2*5}=\frac{5+\sqrt{5}}{10} $
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