5=-1/2x^2+4x+1

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Solution for 5=-1/2x^2+4x+1 equation: 


x in (-oo:+oo)

5 = (-1/2)*x^2+4*x+1 // - (-1/2)*x^2+4*x+1

5-((-1/2)*x^2)-(4*x)-1 = 0

(1/2)*x^2-4*x-1+5 = 0

1/2*x^2-4*x+4 = 0

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

DELTA = 8

DELTA > 0

x = (8^(1/2)+4)/(1/2*2) or x = (4-8^(1/2))/(1/2*2)

x = 2*2^(1/2)+4 or x = 4-2*2^(1/2)

x in { 4-2*2^(1/2), 2*2^(1/2)+4 }

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