y=4(x^2-7/4x)-5

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Solution for y=4(x^2-7/4x)-5 equation: 


x in (-oo:+oo)

y = 4*(x^2-((7/4)*x))-5 // - 4*(x^2-((7/4)*x))-5

y-(4*(x^2-((7/4)*x)))+5 = 0

y-4*(x^2+(-7/4)*x)+5 = 0

y-4*(x^2-7/4*x)+5 = 0

y-4*(x^2-7/4*x)+5 = 0

7*x-4*x^2+y+5 = 0

7*x-4*x^2+y+5 = 0

7*x-4*x^2+y+5 = 0

DELTA = 7^2-(-4*4*(y+5))

DELTA = 16*(y+5)+49

16*(y+5)+49 = 0

16*(y+5)+49 = 0

16*y+129 = 0

16*y+129 = 0

16*y+129 = 0 // - 129

16*y = -129 // : 16

y = -129/16

DELTA = 0  <=>  t_3 = -129/16

x = -7/(-4*2) i y = -129/16

x = 7/8 i y = -129/16

( x = ((16*(y+5)+49)^(1/2)-7)/(-4*2) or x = (-(16*(y+5)+49)^(1/2)-7)/(-4*2) ) i y > -129/16

( x = ((16*(y+5)+49)^(1/2)-7)/(-8) or x = ((16*(y+5)+49)^(1/2)+7)/8 ) i y > -129/16

y-(-129/16) > 0

y+129/16 > 0

y+129/16 > 0 // - 129/16

y > -129/16

x in { 7/8, ((16*(y+5)+49)^(1/2)-7)/(-8), ((16*(y+5)+49)^(1/2)+7)/8 }

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