400=(0.1(x)^2+3(t))/x

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Solution for 400=(0.1(x)^2+3(t))/x equation: 


D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

400 = (3*t+0.1*x^2)/x // - (3*t+0.1*x^2)/x

400-((3*t+0.1*x^2)/x) = 0

(-1*(3*t+0.1*x^2))/x+400 = 0

(-1*(3*t+0.1*x^2))/x+(400*x)/x = 0

400*x-1*(3*t+0.1*x^2) = 0

400*x-3*t-0.1*x^2 = 0

(400*x-3*t-0.1*x^2)/x = 0

(400*x-3*t-0.1*x^2)/x = 0 // * x

400*x-3*t-0.1*x^2 = 0

400*x-3*t-0.1*x^2 = 0

DELTA = 400^2-(-3*(-0.1)*4*t)

DELTA = 160000-1.2*t

160000-1.2*t = 0

160000-1.2*t = 0 // - 160000

-1.2*t = -160000 // : -1.2

t = -160000/(-1.2)

t = 133333.33333333

DELTA = 0  <=>  t_3 = 133333.33333333

x = -400/(-0.1*2) i t = 133333.33333333

x = 2000 i t = 133333.33333333

( x = ((160000-1.2*t)^(1/2)-400)/(-0.1*2) or x = (-(160000-1.2*t)^(1/2)-400)/(-0.1*2) ) i t > 133333.33333333

( x = -5*((160000-1.2*t)^(1/2)-400) or x = 5*((160000-1.2*t)^(1/2)+400) ) i t > 133333.33333333

t-133333.33333333 > 0

t-133333.33333333 > 0 // + 133333.33333333

t > 133333.33333333

x in { 2000, -5*((160000-1.2*t)^(1/2)-400), 5*((160000-1.2*t)^(1/2)+400) }

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