45.9=(2x^2)/(3-x)^2

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Solution for 45.9=(2x^2)/(3-x)^2 equation: 


D( x )

(3-x)^2 = 0

(3-x)^2 = 0

(3-x)^2 = 0

3-x = 0 // - 3

-x = -3 // * -1

x = 3

x in (-oo:3) U (3:+oo)

45.9 = (2*x^2)/((3-x)^2) // - (2*x^2)/((3-x)^2)

45.9-((2*x^2)/((3-x)^2)) = 0

45.9-2*x^2*(3-x)^-2 = 0

(-2*x^2)/((3-x)^2)+45.9 = 0

(-2*x^2)/((3-x)^2)+(45.9*(3-x)^2)/((3-x)^2) = 0

45.9*(3-x)^2-2*x^2 = 0

43.9*x^2-275.4*x+413.1 = 0

43.9*x^2-275.4*x+413.1 = 0

43.9*x^2-275.4*x+413.1 = 0

DELTA = (-275.4)^2-(4*43.9*413.1)

DELTA = 275.4^2-72540.36

DELTA = 3304.8

DELTA > 0

x = ((275.4^2-72540.36)^(1/2)+275.4)/(2*43.9) or x = (275.4-(275.4^2-72540.36)^(1/2))/(2*43.9)

x = 0.01138952*((275.4^2-72540.36)^(1/2)+275.4) or x = 0.01138952*(275.4-(275.4^2-72540.36)^(1/2))

(x-0.01138952*(275.4-(275.4^2-72540.36)^(1/2)))*(x-0.01138952*((275.4^2-72540.36)^(1/2)+275.4)) = 0

((x-0.01138952*(275.4-(275.4^2-72540.36)^(1/2)))*(x-0.01138952*((275.4^2-72540.36)^(1/2)+275.4)))/((3-x)^2) = 0

((x-0.01138952*(275.4-(275.4^2-72540.36)^(1/2)))*(x-0.01138952*((275.4^2-72540.36)^(1/2)+275.4)))/((3-x)^2) = 0 // * (3-x)^2

(x-0.01138952*(275.4-(275.4^2-72540.36)^(1/2)))*(x-0.01138952*((275.4^2-72540.36)^(1/2)+275.4)) = 0

( x-0.01138952*((275.4^2-72540.36)^(1/2)+275.4) )

x-0.01138952*((275.4^2-72540.36)^(1/2)+275.4) = 0 // + -0.01138952*((275.4^2-72540.36)^(1/2)+275.4)

x = -(-0.01138952*((275.4^2-72540.36)^(1/2)+275.4))

x = 0.01138952*((275.4^2-72540.36)^(1/2)+275.4)

( x-0.01138952*(275.4-(275.4^2-72540.36)^(1/2)) )

x-0.01138952*(275.4-(275.4^2-72540.36)^(1/2)) = 0 // + -0.01138952*(275.4-(275.4^2-72540.36)^(1/2))

x = -(-0.01138952*(275.4-(275.4^2-72540.36)^(1/2)))

x = 0.01138952*(275.4-(275.4^2-72540.36)^(1/2))

x in { 0.01138952*((275.4^2-72540.36)^(1/2)+275.4), 0.01138952*(275.4-(275.4^2-72540.36)^(1/2)) }

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