The simplest way to insert spaces in LaTeX equations, it to use ~ (tilde) to create a non breakable space.

As an example, a~b displays : $a~b$ .

For more specific spaces, here is a list of spaces and size in math unit (mu, equal to 1/18 em, where em is taken from the math symbols family):

• \quad space equal to the current font size (= 18 mu)
• \! negative space (-3/18 of \quand = -3 mu)
• \, narrow space (3/18 of \quad = 3 mu)
• \: average space (4/18 of \quad = 4 mu)
• \; wide space (5/18 of = 5 mu)*
• \ (space after backlash) space in normal space
• ~ non breakable space
• \qquad : wider space (double \quad)

Here is an example:

\begin{align}
f(x) =&  ax^2 \! + \! bx \! + \! c \\
f(x) =&  ax^2 + bx + c \\
f(x) =&  ax^2 \, + \, bx \, + \, c \\
f(x) =&  ax^2 \: + \: bx \: + \: c \\
f(x) =&  ax^2 \; + \: bx \; + \; c \\
f(x) =&  ax^2 \  + \  bx \  + \  c \\
f(x) =&  ax^2 ~ + ~ bx ~ + ~ c \\
f(x) =& ax^2 \quad  + \quad  bx \quad  + \quad  c \\
f(x) =& ax^2 \qquad  + \qquad  bx \qquad  + \qquad  c 
\end{align}

The previous code displays:

$$\begin{align} f(x) =& ax^2 \! + \! bx \! + \! c \\ f(x) =& ax^2 + bx + c \\ f(x) =& ax^2 \, + \, bx \, + \, c \\ f(x) =& ax^2 \: + \: bx \: + \: c \\ f(x) =& ax^2 \; + \: bx \; + \; c \\ f(x) =& ax^2 \ + \ bx \ + \ c \\ f(x) =& ax^2 ~ + ~ bx ~ + ~ c \\ f(x) =& ax^2 \quad + \quad bx \quad + \quad c \\ f(x) =& ax^2 \qquad + \qquad bx \qquad + \qquad c \end{align}$$