(2575+(2575+50*(n-1)))/2*n=76050

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Solution for (2575+(2575+50*(n-1)))/2*n=76050 equation: 


n in (-oo:+oo)

n*((50*(n-1)+2575+2575)/2) = 76050 // - 76050

n*((50*(n-1)+2575+2575)/2)-76050 = 0

(n*(50*(n-1)+2575+2575))/2-76050 = 0

(n*(50*(n-1)+2575+2575))/2+(-76050*2)/2 = 0

n*(50*(n-1)+2575+2575)-76050*2 = 0

50*n^2+5100*n-152100 = 0

50*n^2+5100*n-152100 = 0

50*(n^2+102*n-3042) = 0

n^2+102*n-3042 = 0

DELTA = 102^2-(-3042*1*4)

DELTA = 22572

DELTA > 0

n = (22572^(1/2)-102)/(1*2) or n = (-22572^(1/2)-102)/(1*2)

n = (6*627^(1/2)-102)/2 or n = (-6*627^(1/2)-102)/2

50*(n-((-6*627^(1/2)-102)/2))*(n-((6*627^(1/2)-102)/2)) = 0

(50*(n-((-6*627^(1/2)-102)/2))*(n-((6*627^(1/2)-102)/2)))/2 = 0

(50*(n-((-6*627^(1/2)-102)/2))*(n-((6*627^(1/2)-102)/2)))/2 = 0 // * 2

50*(n-((-6*627^(1/2)-102)/2))*(n-((6*627^(1/2)-102)/2)) = 0

( n-((-6*627^(1/2)-102)/2) )

n-((-6*627^(1/2)-102)/2) = 0 // + (-6*627^(1/2)-102)/2

n = (-6*627^(1/2)-102)/2

( n-((6*627^(1/2)-102)/2) )

n-((6*627^(1/2)-102)/2) = 0 // + (6*627^(1/2)-102)/2

n = (6*627^(1/2)-102)/2

n in { (-6*627^(1/2)-102)/2, (6*627^(1/2)-102)/2 }

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