(2x)(x+1)/2=12

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Solution for (2x)(x+1)/2=12 equation: 


x in (-oo:+oo)

(2*x*(x+1))/2 = 12 // - 12

(2*x*(x+1))/2-12 = 0

(2*x*(x+1))/2+(-12*2)/2 = 0

2*x*(x+1)-12*2 = 0

2*x^2+2*x-24 = 0

2*x^2+2*x-24 = 0

2*(x^2+x-12) = 0

x^2+x-12 = 0

DELTA = 1^2-(-12*1*4)

DELTA = 49

DELTA > 0

x = (49^(1/2)-1)/(1*2) or x = (-49^(1/2)-1)/(1*2)

x = 3 or x = -4

2*(x+4)*(x-3) = 0

(2*(x+4)*(x-3))/2 = 0

(2*(x+4)*(x-3))/2 = 0 // * 2

2*(x+4)*(x-3) = 0

( x+4 )

x+4 = 0 // - 4

x = -4

( x-3 )

x-3 = 0 // + 3

x = 3

x in { -4, 3 }

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