3(x-z)-3+(x-z)/2+(x-z)2

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Solution for 3(x-z)-3+(x-z)/2+(x-z)2 equation: 


x in (-oo:+oo)

3*(x-z)+(x-z)/2+(x-z)^2-3 = 0

(2*3*(x-z))/2+(x-z)/2+(2*(x-z)^2)/2+(-3*2)/2 = 0

2*3*(x-z)+2*(x-z)^2+x-z-3*2 = 0

2*x^2+7*x-7*z-4*x*z+2*z^2-6 = 0

(2*x^2+7*x-7*z-4*x*z+2*z^2-6)/2 = 0

(2*x^2+7*x-7*z-4*x*z+2*z^2-6)/2 = 0 // * 2

2*x^2+7*x-7*z-4*x*z+2*z^2-6 = 0

2*x^2-4*x*z+2*z^2-7*z-6 = 0

DELTA = (-4*z)^2-(2*4*(2*z^2-7*z-6))

DELTA = 16*z^2-8*(2*z^2-7*z-6)

16*z^2-8*(2*z^2-7*z-6) = 0

16*z^2-8*(2*z^2-7*z-6) = 0

56*z+48 = 0

56*z+48 = 0

56*z+48 = 0 // - 48

56*z = -48 // : 56

z = -48/56

z = -6/7

DELTA = 0  <=>  t_3 = -6/7

x = (-(-4*z))/(2*2) i z = -6/7

x = z i z = -6/7

( x = ((16*z^2-8*(2*z^2-7*z-6))^(1/2)-(-4*z))/(2*2) or x = (-(16*z^2-8*(2*z^2-7*z-6))^(1/2)-(-4*z))/(2*2) ) i z > -6/7

( x = ((16*z^2-8*(2*z^2-7*z-6))^(1/2)+4*z)/4 or x = (4*z-(16*z^2-8*(2*z^2-7*z-6))^(1/2))/4 ) i z > -6/7

z+6/7 > 0

z+6/7 > 0 // - 6/7

z > -6/7

x in { z, ((16*z^2-8*(2*z^2-7*z-6))^(1/2)+4*z)/4, (4*z-(16*z^2-8*(2*z^2-7*z-6))^(1/2))/4 }

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