4x^2+11x+2/(x+2)

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Solution for 4x^2+11x+2/(x+2) equation:


D( x )

x+2 = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x in (-oo:-2) U (-2:+oo)

t_1 = 0

2/(x+2)+t_1+4*x^2+11*x = 0

2/(x+2)+(t_1*(x+2))/(x+2)+(4*x^2*(x+2))/(x+2)+(11*x*(x+2))/(x+2) = 0

t_1*(x+2)+4*x^2*(x+2)+11*x*(x+2)+2 = 0

t_1*x+2*t_1+4*x^3+8*x^2+11*x^2+22*x+2 = 0

t_1*x+2*t_1+4*x^3+19*x^2+22*x+2 = 0

t_1*x+2*t_1+4*x^3+19*x^2+22*x+2 = 0

t_1*x+2*t_1+4*x^3+19*x^2+22*x+2

2*(t_1+1)+t_1*x+4*x^3+19*x^2+22*x

x*(t_1+4*x^2)+2*(t_1+1)+19*x^2+22*x

x*(19*x+22)+x*(t_1+4*x^2)+2*(t_1+1)

x*(t_1+4*x^2+19*x+22)+2*(t_1+1)

3*(t_1+4*x^2+19*x+22)

(3*(t_1+4*x^2+19*x+22))/(x+2) = 0

(3*(t_1+4*x^2+19*x+22))/(x+2) = 0 // * x+2

3*(t_1+4*x^2+19*x+22) = 0

t_1+4*x^2+19*x+22 = 0

DELTA = 19^2-(4*4*(t_1+22))

DELTA = 361-16*(t_1+22)

361-16*(t_1+22) = 0

361-16*(t_1+22) = 0

9-16*t_1 = 0

9-16*t_1 = 0

9-16*t_1 = 0 // - 9

-16*t_1 = -9 // : -16

t_1 = -9/(-16)

t_1 = 9/16

DELTA = 0 <=> t_3 = 9/16

x = -19/(2*4) i t_1 = 9/16

x = -19/8 i t_1 = 9/16

( x = ((361-16*(t_1+22))^(1/2)-19)/(2*4) or x = (-(361-16*(t_1+22))^(1/2)-19)/(2*4) ) i t_1 > 9/16

( x = ((361-16*(t_1+22))^(1/2)-19)/8 or x = (-((361-16*(t_1+22))^(1/2)+19))/8 ) i t_1 > 9/16

t_1-9/16 > 0

t_1-9/16 > 0 // + 9/16

t_1 > 9/16

x in { ((361-16*(0+22))^(1/2)-19)/8}

x in { -19/8, (-((361-16*(0+22))^(1/2)+19))/8 }

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