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-(1-5x)x=2
We move all terms to the left:
-(1-5x)x-(2)=0
We add all the numbers together, and all the variables
-(-5x+1)x-2=0
We multiply parentheses
5x^2-x-2=0
We add all the numbers together, and all the variables
5x^2-1x-2=0
a = 5; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·5·(-2)
Δ = 41
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{-(-1)-\sqrt{41}}{2*5}=\frac{1-\sqrt{41}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{41}}{2*5}=\frac{1+\sqrt{41}}{10} $
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