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

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


x in (-oo:+oo)

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

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

((2*x-5)^2)/25-x+3 = 0

((2*x-5)^2)/25+(25*(-x))/25+(3*25)/25 = 0

(2*x-5)^2+25*(-x)+3*25 = 0

4*x^2-45*x+25+75 = 0

4*x^2-45*x+100 = 0

4*x^2-45*x+100 = 0

4*x^2-45*x+100 = 0

DELTA = (-45)^2-(4*4*100)

DELTA = 425

DELTA > 0

x = (425^(1/2)+45)/(2*4) or x = (45-425^(1/2))/(2*4)

x = (5*17^(1/2)+45)/8 or x = (45-5*17^(1/2))/8

(x-((45-5*17^(1/2))/8))*(x-((5*17^(1/2)+45)/8)) = 0

((x-((45-5*17^(1/2))/8))*(x-((5*17^(1/2)+45)/8)))/25 = 0

((x-((45-5*17^(1/2))/8))*(x-((5*17^(1/2)+45)/8)))/25 = 0 // * 25

(x-((45-5*17^(1/2))/8))*(x-((5*17^(1/2)+45)/8)) = 0

( x-((45-5*17^(1/2))/8) )

x-((45-5*17^(1/2))/8) = 0 // + (45-5*17^(1/2))/8

x = (45-5*17^(1/2))/8

( x-((5*17^(1/2)+45)/8) )

x-((5*17^(1/2)+45)/8) = 0 // + (5*17^(1/2)+45)/8

x = (5*17^(1/2)+45)/8

x in { (45-5*17^(1/2))/8, (5*17^(1/2)+45)/8 }

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