Y=1/2(3x+5)(7x+4)

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Solution for Y=1/2(3x+5)(7x+4) equation: 


x in (-oo:+oo)

Y = (1/2)*(3*x+5)*(7*x+4) // - (1/2)*(3*x+5)*(7*x+4)

Y-((1/2)*(3*x+5)*(7*x+4)) = 0

(-1/2)*(7*x+4)*(3*x+5)+Y = 0

Y-1/2*(7*x+4)*(3*x+5) = 0

Y-1/2*(7*x+4)*(3*x+5) = 0

Y-21/2*x^2-47/2*x-10 = 0

Y-21/2*x^2-47/2*x-10 = 0

Y-21/2*x^2-47/2*x-10 = 0

DELTA = (-47/2)^2-(-21/2*4*(Y-10))

DELTA = 42*(Y-10)+2209/4

42*(Y-10)+2209/4 = 0

(4*42*(Y-10))/4+2209/4 = 0

4*42*(Y-10)+2209 = 0

168*Y+529 = 0

(168*Y+529)/4 = 0

(168*Y+529)/4 = 0 // * 4

168*Y+529 = 0

168*Y+529 = 0 // - 529

168*Y = -529 // : 168

Y = -529/168

DELTA = 0  <=>  t_3 = -529/168

x = 47/2/(-21/2*2) i Y = -529/168

x = -47/42 i Y = -529/168

( x = ((42*(Y-10)+2209/4)^(1/2)+47/2)/(-21/2*2) or x = (47/2-(42*(Y-10)+2209/4)^(1/2))/(-21/2*2) ) i Y > -529/168

( x = ((42*(Y-10)+2209/4)^(1/2)+47/2)/(-21) or x = (47/2-(42*(Y-10)+2209/4)^(1/2))/(-21) ) i Y > -529/168

Y-(-529/168) > 0

Y+529/168 > 0

Y+529/168 > 0 // - 529/168

Y > -529/168

x in { -47/42, ((42*(Y-10)+2209/4)^(1/2)+47/2)/(-21), (47/2-(42*(Y-10)+2209/4)^(1/2))/(-21) }

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