(X^2-9)-(x-3)/5(x-3)

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Solution for (X^2-9)-(x-3)/5(x-3) equation: 


x in (-oo:+oo)

t_1 = X^2-9

(-1/5)*(x-3)^2+t_1 = 0

t_1-1/5*(x-3)^2 = 0

t_1-1/5*(x-3)^2 = 0

t_1-1/5*x^2+6/5*x-9/5 = 0

t_1-1/5*x^2+6/5*x-9/5 = 0

t_1-1/5*x^2+6/5*x-9/5 = 0

DELTA = (6/5)^2-(-1/5*4*(t_1-9/5))

DELTA = 4/5*(t_1-9/5)+36/25

4/5*(t_1-9/5)+36/25 = 0

(4/5*25*(t_1-9/5))/25+36/25 = 0

4/5*25*(t_1-9/5)+36 = 0

20*t_1 = 0

(20*t_1)/25 = 0

(20*t_1)/25 = 0 // * 25

20*t_1 = 0

20*t_1 = 0 // : 20

t_1 = 0

DELTA = 0  <=>  t_4 = 0

x = -6/5/(-1/5*2) i t_1 = 0

x = 3 i t_1 = 0

( x = ((4/5*(t_1-9/5)+36/25)^(1/2)-6/5)/(-1/5*2) or x = (-(4/5*(t_1-9/5)+36/25)^(1/2)-6/5)/(-1/5*2) ) i t_1 > 0

( x = -5/2*((4/5*(t_1-9/5)+36/25)^(1/2)-6/5) or x = 5/2*((4/5*(t_1-9/5)+36/25)^(1/2)+6/5) ) i t_1 > 0

t_1+0 > 0

t_1 > 0

t_1+0 > 0 // - 0

t_1 > 0

x in { 3, -5/2*((4/5*(X^2-9-9/5)+36/25)^(1/2)-6/5), 5/2*((4/5*(X^2-9-9/5)+36/25)^(1/2)+6/5) }

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