(5/2x)-((x-3)/3x)=(5/6)

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Solution for (5/2x)-((x-3)/3x)=(5/6) equation:


x in (-oo:+oo)

(5/2)*x-(x*((x-3)/3)) = 5/6 // - 5/6

(5/2)*x-(x*((x-3)/3))-(5/6) = 0

(5/2)*x-(x*((x-3)/3))-5/6 = 0

(-1*x*(x-3))/3+(5*x)/2-5/6 = 0

(-1*2*6*x*(x-3))/(2*3*6)+(3*5*6*x)/(2*3*6)+(-5*2*3)/(2*3*6) = 0

3*5*6*x-1*2*6*x*(x-3)-5*2*3 = 0

126*x-12*x^2-30 = 0

126*x-12*x^2-30 = 0

6*(21*x-2*x^2-5) = 0

21*x-2*x^2-5 = 0

DELTA = 21^2-(-5*(-2)*4)

DELTA = 401

DELTA > 0

x = (401^(1/2)-21)/(-2*2) or x = (-401^(1/2)-21)/(-2*2)

x = (401^(1/2)-21)/(-4) or x = (401^(1/2)+21)/4

6*(x-((401^(1/2)-21)/(-4)))*(x-((401^(1/2)+21)/4)) = 0

(6*(x-((401^(1/2)-21)/(-4)))*(x-((401^(1/2)+21)/4)))/(2*3*6) = 0

(6*(x-((401^(1/2)-21)/(-4)))*(x-((401^(1/2)+21)/4)))/(2*3*6) = 0 // * 2*3*6

6*(x-((401^(1/2)-21)/(-4)))*(x-((401^(1/2)+21)/4)) = 0

( x-((401^(1/2)+21)/4) )

x-((401^(1/2)+21)/4) = 0 // + (401^(1/2)+21)/4

x = (401^(1/2)+21)/4

( x-((401^(1/2)-21)/(-4)) )

x-((401^(1/2)-21)/(-4)) = 0 // + (401^(1/2)-21)/(-4)

x = (401^(1/2)-21)/(-4)

x in { (401^(1/2)+21)/4, (401^(1/2)-21)/(-4) }

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