(X-20)+40(x-10)1/3x

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Solution for (X-20)+40(x-10)1/3x equation: 


x in (-oo:+oo)

x*((40*(x-10)^1)/3)+X-20 = 0

x*((40*(x-10))/3)+X-20 = 0

(40*x*(x-10))/3+X-20 = 0

(40*x*(x-10))/3+(3*X)/3+(-20*3)/3 = 0

40*x*(x-10)+3*X-20*3 = 0

3*X+40*x^2-400*x-60 = 0

(3*X+40*x^2-400*x-60)/3 = 0

(3*X+40*x^2-400*x-60)/3 = 0 // * 3

3*X+40*x^2-400*x-60 = 0

3*X+40*x^2-400*x-60 = 0

DELTA = (-400)^2-(4*40*(3*X-60))

DELTA = 160000-160*(3*X-60)

160000-160*(3*X-60) = 0

160000-160*(3*X-60) = 0

169600-480*X = 0

169600-480*X = 0

169600-480*X = 0 // - 169600

-480*X = -169600 // : -480

X = -169600/(-480)

X = 1060/3

DELTA = 0  <=>  t_3 = 1060/3

x = 400/(2*40) i X = 1060/3

x = 5 i X = 1060/3

( x = ((160000-160*(3*X-60))^(1/2)+400)/(2*40) or x = (400-(160000-160*(3*X-60))^(1/2))/(2*40) ) i X > 1060/3

( x = ((160000-160*(3*X-60))^(1/2)+400)/80 or x = (400-(160000-160*(3*X-60))^(1/2))/80 ) i X > 1060/3

X-1060/3 > 0

X-1060/3 > 0 // + 1060/3

X > 1060/3

x in { 5, ((160000-160*(3*X-60))^(1/2)+400)/80, (400-(160000-160*(3*X-60))^(1/2))/80 }

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