x^2(7x+51)/40=x

Solution for x^2(7x+51)/40=x equation:

x in (-oo:+oo)

(x^2*(7*x+51))/40 = x // - x

(x^2*(7*x+51))/40-x = 0

(x^2*(7*x+51))/40+(40*(-x))/40 = 0

x^2*(7*x+51)+40*(-x) = 0

7*x^3+51*x^2-40*x = 0

7*x^3+51*x^2-40*x = 0

x*(7*x^2+51*x-40) = 0

7*x^2+51*x-40 = 0

DELTA = 51^2-(-40*4*7)

DELTA = 3721

DELTA > 0

x = (3721^(1/2)-51)/(2*7) or x = (-3721^(1/2)-51)/(2*7)

x = 5/7 or x = -8

x*(x+8)*(x-5/7) = 0

(x*(x+8)*(x-5/7))/40 = 0

(x*(x+8)*(x-5/7))/40 = 0 // * 40

x*(x+8)*(x-5/7) = 0

( x+8 )

x+8 = 0 // - 8

x = -8

( x-5/7 )

x-5/7 = 0 // + 5/7

x = 5/7

( x )

x = 0

x in { -8, 5/7, 0 }