3/x^2=4/(10-x)^2

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Solution for 3/x^2=4/(10-x)^2 equation: 


D( x )

x^2 = 0

(10-x)^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

(10-x)^2 = 0

(10-x)^2 = 0

10-x = 0 // - 10

-x = -10 // * -1

x = 10

x in (-oo:0) U (0:10) U (10:+oo)

3/(x^2) = 4/((10-x)^2) // - 4/((10-x)^2)

3/(x^2)-(4/((10-x)^2)) = 0

3/(x^2)-4*(10-x)^-2 = 0

3/(x^2)-4/((10-x)^2) = 0

(-4*x^2)/(x^2*(10-x)^2)+(3*(10-x)^2)/(x^2*(10-x)^2) = 0

3*(10-x)^2-4*x^2 = 0

300-x^2-60*x = 0

300-x^2-60*x = 0

300-x^2-60*x = 0

DELTA = (-60)^2-(-1*4*300)

DELTA = 4800

DELTA > 0

x = (4800^(1/2)+60)/(-1*2) or x = (60-4800^(1/2))/(-1*2)

x = (40*3^(1/2)+60)/(-2) or x = (60-40*3^(1/2))/(-2)

(x-((40*3^(1/2)+60)/(-2)))*(x-((60-40*3^(1/2))/(-2))) = 0

((x-((40*3^(1/2)+60)/(-2)))*(x-((60-40*3^(1/2))/(-2))))/(x^2*(10-x)^2) = 0

((x-((40*3^(1/2)+60)/(-2)))*(x-((60-40*3^(1/2))/(-2))))/(x^2*(10-x)^2) = 0 // * x^2*(10-x)^2

(x-((40*3^(1/2)+60)/(-2)))*(x-((60-40*3^(1/2))/(-2))) = 0

( x-((40*3^(1/2)+60)/(-2)) )

x-((40*3^(1/2)+60)/(-2)) = 0 // + (40*3^(1/2)+60)/(-2)

x = (40*3^(1/2)+60)/(-2)

( x-((60-40*3^(1/2))/(-2)) )

x-((60-40*3^(1/2))/(-2)) = 0 // + (60-40*3^(1/2))/(-2)

x = (60-40*3^(1/2))/(-2)

x in { (40*3^(1/2)+60)/(-2), (60-40*3^(1/2))/(-2) }

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