f=9x^2-4/3x-2

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Solution for f=9x^2-4/3x-2 equation: 


x in (-oo:+oo)

f = 9*x^2-((4/3)*x)-2 // - 9*x^2-((4/3)*x)-2

f-(9*x^2)+(4/3)*x+2 = 0

f-9*x^2+(4/3)*x+2 = 0

f-9*x^2+4/3*x+2 = 0

DELTA = (4/3)^2-(-9*4*(f+2))

DELTA = 36*(f+2)+16/9

36*(f+2)+16/9 = 0

(9*36*(f+2))/9+16/9 = 0

9*36*(f+2)+16 = 0

324*f+664 = 0

(324*f+664)/9 = 0

(324*f+664)/9 = 0 // * 9

324*f+664 = 0

324*f+664 = 0 // - 664

324*f = -664 // : 324

f = -664/324

f = -166/81

DELTA = 0  <=>  t_1 = -166/81

x = -4/3/(-9*2) i f = -166/81

x = 2/27 i f = -166/81

( x = ((36*(f+2)+16/9)^(1/2)-4/3)/(-9*2) or x = (-(36*(f+2)+16/9)^(1/2)-4/3)/(-9*2) ) i f > -166/81

( x = ((36*(f+2)+16/9)^(1/2)-4/3)/(-18) or x = ((36*(f+2)+16/9)^(1/2)+4/3)/18 ) i f > -166/81

f+166/81 > 0

f+166/81 > 0 // - 166/81

f > -166/81

x in { 2/27, ((36*(f+2)+16/9)^(1/2)-4/3)/(-18), ((36*(f+2)+16/9)^(1/2)+4/3)/18 }

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