! Missing delimiter (. inserted).

Question

I can't figure out why my code won't work. I need an answer as soon as possible.
[
begin{split}
therefore delta F left(E_{x} right )&=int left [ frac{partial F}{partial E }delta E+frac{partial F}{partialdot{E}}delta dot{E}right ]dx=0
&=intleft {left[frac{partial H_{z}}{partial y}-frac{partial H_{y}}{partial x}-2iomegavarepsilon_{0}varepsilon E_{x} right ]delta E_{x}-left[ frac{partial}{partial x}left ( frac{partial F}{partial E/partial x}right )+frac{partial}{partial y}left ( frac{partial F}{partial E/partial y}right )+frac{partial}{partial z}left ( frac{partial F}{partial E/partial z}right )right ]delta E_{x}right }  dx
&=intleft[left(frac{partial H_{z}}{partial y}-frac{partial H_{y}}{partial x}-2iomegavarepsilon_{0}varepsilon E_{x} right ) - left(-frac{partial H_{z}}{partial y}+frac{partial H_{y}}{partial x} right )right ]delta E_{x}  dx
&=int 2 (frac{partial H_{z}}{partial y}-frac{partial H_{y}}{partial x}-iomegavarepsilon_{0}varepsilon E_{x})delta E_{x}  dx &=0.
end{split}
]

The error I get is:
! Missing delimiter (. inserted).

{
l.50     end{split}
Please help!

egreg · Answer

You have some misplaced  before E_x
I'd avoid left and right for this display, preferring bigg size. In any case, left and right cannot straddle different parts of the alignment.
documentclass{article}
usepackage{amsmath,amssymb}

newcommand{pder}[2]{frac{partial #1}{partial #2}}

begin{document}

[
begin{split}
therefore delta F(E_{x})
  &=int biggl[ pder{F}{E}delta E+pder{F}{dot{E}}delta dot{E} biggr],dx=0 [2ex]
  &=int
    biggl{
      biggl[
        pder{H_{z}}{y}-pder{H_{y}}{x}-2iomegavarepsilon_{0}varepsilon E_{x}
      biggr]delta E_{x} 
  &qquadquad
      -biggl[
        pder{}{x}
        biggl( pder{F}{E/partial x} biggr)+pder{}{y} biggl( pder{F}{E/partial y} biggr)
        +pder{}{z} biggl( pder{F}{E/partial z} biggr)
      biggr]delta E_{x}
    biggr},dx [2ex]
  &=int
    biggl[
      biggl(pder{H_{z}}{y}-pder{H_{y}}{x}-2iomegavarepsilon_{0}varepsilon E_{x} biggr)
      -
      biggl(-pder{H_{z}}{y}+pder{H_{y}}{x} biggr)
    biggr]delta E_{x} , dx[2ex]
&=int 2
  biggl(
    pder{H_{z}}{y}-pder{H_{y}}{x}-iomegavarepsilon_{0}varepsilon E_{x}
  biggr)delta E_{x} , dx[2ex]
& =0.
end{split}
]

end{document}

The second integral needs to be split across lines, I added some spacing to make clear that the third line is a continuation of the second one and also added vertical spaces between main lines.
An abbreviation for partial derivatives has been defined, to ease input.

I'd also omit the therefore symbol: just spell out “therefore” before the display.

! Missing delimiter (. inserted).

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