A=1/2(12x^2-7x-10)

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Solution for A=1/2(12x^2-7x-10) equation: 


x in (-oo:+oo)

A = (1/2)*(12*x^2-(7*x)-10) // - (1/2)*(12*x^2-(7*x)-10)

A-((1/2)*(12*x^2-(7*x)-10)) = 0

(-1/2)*(12*x^2-7*x-10)+A = 0

A-1/2*(12*x^2-7*x-10) = 0

A-1/2*(12*x^2-7*x-10) = 0

A-6*x^2+7/2*x+5 = 0

A-6*x^2+7/2*x+5 = 0

A-6*x^2+7/2*x+5 = 0

DELTA = (7/2)^2-(-6*4*(A+5))

DELTA = 24*(A+5)+49/4

24*(A+5)+49/4 = 0

(4*24*(A+5))/4+49/4 = 0

4*24*(A+5)+49 = 0

96*A+529 = 0

(96*A+529)/4 = 0

(96*A+529)/4 = 0 // * 4

96*A+529 = 0

96*A+529 = 0 // - 529

96*A = -529 // : 96

A = -529/96

DELTA = 0  <=>  t_3 = -529/96

x = -7/2/(-6*2) i A = -529/96

x = 7/24 i A = -529/96

( x = ((24*(A+5)+49/4)^(1/2)-7/2)/(-6*2) or x = (-(24*(A+5)+49/4)^(1/2)-7/2)/(-6*2) ) i A > -529/96

( x = ((24*(A+5)+49/4)^(1/2)-7/2)/(-12) or x = ((24*(A+5)+49/4)^(1/2)+7/2)/12 ) i A > -529/96

A-(-529/96) > 0

A+529/96 > 0

A+529/96 > 0 // - 529/96

A > -529/96

x in { 7/24, ((24*(A+5)+49/4)^(1/2)-7/2)/(-12), ((24*(A+5)+49/4)^(1/2)+7/2)/12 }

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