(10/7x-14)^2=20x

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Solution for (10/7x-14)^2=20x equation:


x in (-oo:+oo)

((10/7)*x-14)^2 = 20*x // - 20*x

((10/7)*x-14)^2-(20*x) = 0

((10/7)*x-14)^2-20*x = 0

(10/7*x-14)^2-20*x = 0

(10/7*x-14)^2-20*x = 0

100/49*x^2-60*x+196 = 0

100/49*x^2-60*x+196 = 0

4*(25/49*x^2-15*x+49) = 0

25/49*x^2-15*x+49 = 0

DELTA = (-15)^2-(25/49*4*49)

DELTA = 125

DELTA > 0

x = (125^(1/2)+15)/(25/49*2) or x = (15-125^(1/2))/(25/49*2)

x = 49/50*(5*5^(1/2)+15) or x = 49/50*(15-5*5^(1/2))

4*(x-49/50*(15-5*5^(1/2)))*(x-49/50*(5*5^(1/2)+15)) = 0

4*(x-49/50*(15-5*5^(1/2)))*(x-49/50*(5*5^(1/2)+15)) = 0

( 4 )

4 = 0

x belongs to the empty set

( x-49/50*(15-5*5^(1/2)) )

x-49/50*(15-5*5^(1/2)) = 0 // + -49/50*(15-5*5^(1/2))

x = -(-49/50*(15-5*5^(1/2)))

x = 49/50*(15-5*5^(1/2))

( x-49/50*(5*5^(1/2)+15) )

x-49/50*(5*5^(1/2)+15) = 0 // + -49/50*(5*5^(1/2)+15)

x = -(-49/50*(5*5^(1/2)+15))

x = 49/50*(5*5^(1/2)+15)

x in { 49/50*(15-5*5^(1/2)), 49/50*(5*5^(1/2)+15) }

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