5(x-4)^2/3=125

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Solution for 5(x-4)^2/3=125 equation: 


x in (-oo:+oo)

(5*(x-4)^2)/3 = 125 // - 125

(5*(x-4)^2)/3-125 = 0

(5*(x-4)^2)/3+(-125*3)/3 = 0

5*(x-4)^2-125*3 = 0

5*x^2-40*x-295 = 0

5*x^2-40*x-295 = 0

5*(x^2-8*x-59) = 0

x^2-8*x-59 = 0

DELTA = (-8)^2-(-59*1*4)

DELTA = 300

DELTA > 0

x = (300^(1/2)+8)/(1*2) or x = (8-300^(1/2))/(1*2)

x = (10*3^(1/2)+8)/2 or x = (8-10*3^(1/2))/2

5*(x-((8-10*3^(1/2))/2))*(x-((10*3^(1/2)+8)/2)) = 0

(5*(x-((8-10*3^(1/2))/2))*(x-((10*3^(1/2)+8)/2)))/3 = 0

(5*(x-((8-10*3^(1/2))/2))*(x-((10*3^(1/2)+8)/2)))/3 = 0 // * 3

5*(x-((8-10*3^(1/2))/2))*(x-((10*3^(1/2)+8)/2)) = 0

( 5 )

5 = 0

x belongs to the empty set

( x-((10*3^(1/2)+8)/2) )

x-((10*3^(1/2)+8)/2) = 0 // + (10*3^(1/2)+8)/2

x = (10*3^(1/2)+8)/2

( x-((8-10*3^(1/2))/2) )

x-((8-10*3^(1/2))/2) = 0 // + (8-10*3^(1/2))/2

x = (8-10*3^(1/2))/2

x in { (10*3^(1/2)+8)/2, (8-10*3^(1/2))/2 }

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