(x^2-3x)^1/2=4x^2-12x-3

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Solution for (x^2-3x)^1/2=4x^2-12x-3 equation:


x in (-oo:+oo)

((x^2-(3*x))^1)/2 = 4*x^2-(12*x)-3 // - 4*x^2-(12*x)-3

((x^2-(3*x))^1)/2-(4*x^2)+12*x+3 = 0

(x^2-3*x)/2-4*x^2+12*x+3 = 0

(x^2-3*x)/2+(-4*2*x^2)/2+(2*12*x)/2+(2*3)/2 = 0

x^2-4*2*x^2-3*x+2*12*x+2*3 = 0

24*x-7*x^2-3*x+6 = 0

21*x-7*x^2+6 = 0

21*x-7*x^2+6 = 0

21*x-7*x^2+6 = 0

DELTA = 21^2-(-7*4*6)

DELTA = 609

DELTA > 0

x = (609^(1/2)-21)/(-7*2) or x = (-609^(1/2)-21)/(-7*2)

x = (609^(1/2)-21)/(-14) or x = (609^(1/2)+21)/14

(x-((609^(1/2)-21)/(-14)))*(x-((609^(1/2)+21)/14)) = 0

((x-((609^(1/2)-21)/(-14)))*(x-((609^(1/2)+21)/14)))/2 = 0

((x-((609^(1/2)-21)/(-14)))*(x-((609^(1/2)+21)/14)))/2 = 0 // * 2

(x-((609^(1/2)-21)/(-14)))*(x-((609^(1/2)+21)/14)) = 0

( x-((609^(1/2)+21)/14) )

x-((609^(1/2)+21)/14) = 0 // + (609^(1/2)+21)/14

x = (609^(1/2)+21)/14

( x-((609^(1/2)-21)/(-14)) )

x-((609^(1/2)-21)/(-14)) = 0 // + (609^(1/2)-21)/(-14)

x = (609^(1/2)-21)/(-14)

x in { (609^(1/2)+21)/14, (609^(1/2)-21)/(-14) }

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