x+(x+1)=1/2(x+1)(x+2)

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


x in (-oo:+oo)

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

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

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

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

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

x-1/2*x^2-1/2*x-1+1 = 0

1/2*x-1/2*x^2-1+1 = 0

1/2*x-1/2*x^2 = 0

1/2*x-1/2*x^2 = 0

1/2*x*(1-x) = 0

1-x = 0 // - 1

-x = -1 // * -1

x = 1

1/2*x*(x-1) = 0

1/2*x*(x-1) = 0

( 1/2*x )

1/2*x = 0 // : 1/2

x = 0

( x-1 )

x-1 = 0 // + 1

x = 1

x in { 0, 1 }

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