v = SQR( 2.e.U / m )
m = mo / SQR( 1 - v^2 / c^2 )
m . v^2 = 2.e.U
mo . v^2 / SQR( 1 - v^2 / c^2 ) = 2.e.U / ()^2
mo^2 . v^4 / ( 1 - v^2 / c^2 ) = 4.e^2.U^2
mo^2 . v^4 = 4.e^2.U^2 . ( 1 - v^2 / c^2 )
mo^2 . v^4 = 4.e^2.U^2 - 4.e^2.U^2 . v^2 / c^2
mo^2 . v^4 + 4.e^2.U^2 . v^2 / c^2 = 4.e^2.U^2
a = mo^2
b = 4.e^2.U^2 / c^2
c = 4.e^2.U^2
a . x^4 + b . x^2 = c
ax^4 + bx^2 - c = 0
u = x^2
au^2 + bu - c = 0
u = -b +/- SQR( b^2 - 4a(-c) ) / 2a
x^2 = -b +/- SQR( b^2 - 4a(-c) ) / 2a
x^2 = - (4.e^2.U^2 / c^2 ) +/- SQR( (4.e^2.U^2 / c^2 )^2 - 4.mo^2 . (-4.e^2.U^2) ) / (2.mo^2)
x^2 = - (2.e.U/c )^2 +/- SQR((2.e.U/c)^4 + (2.mo.2.e.U)^2 ) / (2.mo^2)
x^2 = - (2.e.U/c )^2 +/- SQR((2.e.U/c)^4 + (4.mo.e.U)^2 ) / (2.mo^2)
x^2 = -(2.e.U/c )^2 +/- SQR((2.e.U/c)^4 + (4.mo.e.U)^2 ) / (2.mo^2)
x = SQR(-(2.e.U/c )^2 +/- SQR((2.e.U/c)^4 + (4.mo.e.U)^2 ) / (2.mo^2))
x^2 = - (2.e.U/c )^2 +/- SQR((2.e.U/c)^4 + (4.mo.e.U)^2 ) / (2.mo^2)
x^2 = -(2.e.U/c )^2 +/- SQR((2.e.U/c)^4 + (4.mo.e.U)^2 ) / (2.mo^2)
x = SQR(-(2.e.U/c )^2 +/- SQR((2.e.U/c)^4 + (4.mo.e.U)^2 ) / (2.mo^2))
v = SQR(-(2.e.U/c )^2 +/- SQR((2.e.U/c)^4 + (4.mo.e.U)^2 ) / (2.mo^2))
