10(x-1)/2x+10x=5

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Solution for 10(x-1)/2x+10x=5 equation: 


x in (-oo:+oo)

x*((10*(x-1))/2)+10*x = 5 // - 5

x*((10*(x-1))/2)+10*x-5 = 0

(10*x*(x-1))/2+10*x-5 = 0

(10*x*(x-1))/2+(2*10*x)/2+(-5*2)/2 = 0

10*x*(x-1)+2*10*x-5*2 = 0

10*x^2+(20-10)*x-10 = 0

10*x^2+(20-10)*x-10 = 0

10*x^2+(20-10)*x-10 = 0

DELTA = (20-10)^2-(-10*4*10)

DELTA = 100+400

DELTA = 500

DELTA > 0

x = ((100+400)^(1/2)-20+10)/(2*10) or x = (10-(100+400)^(1/2)-20)/(2*10)

x = ((100+400)^(1/2)-20+10)/20 or x = (10-(100+400)^(1/2)-20)/20

(x-((10-(100+400)^(1/2)-20)/20))*(x-(((100+400)^(1/2)-20+10)/20)) = 0

((x-((10-(100+400)^(1/2)-20)/20))*(x-(((100+400)^(1/2)-20+10)/20)))/2 = 0

((x-((10-(100+400)^(1/2)-20)/20))*(x-(((100+400)^(1/2)-20+10)/20)))/2 = 0 // * 2

(x-((10-(100+400)^(1/2)-20)/20))*(x-(((100+400)^(1/2)-20+10)/20)) = 0

( x-(((100+400)^(1/2)-20+10)/20) )

x-(((100+400)^(1/2)-20+10)/20) = 0 // + ((100+400)^(1/2)-20+10)/20

x = ((100+400)^(1/2)-20+10)/20

( x-((10-(100+400)^(1/2)-20)/20) )

x-((10-(100+400)^(1/2)-20)/20) = 0 // + (10-(100+400)^(1/2)-20)/20

x = (10-(100+400)^(1/2)-20)/20

x in { ((100+400)^(1/2)-20+10)/20, (10-(100+400)^(1/2)-20)/20 }

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