Equation Editing

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When a is uneqal to 0, there are exactly two solutions to ax² + bx + c = 0 and they are

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

source code

 [asciimath]
 --
   x = {-b \pm \sqrt{b^2-4ac} \over 2a}
 --

\dot{x} = σ (y - x)

\dot{y} = ρ x - y - x z

\dot{z} = - β z + x y

source code

  [asciimath]
  --
    \dot{x}  = \sigma(y-x)
  --

(\sum_{k = 1}^{n} a_{k} b_{k})^{2} \leq (\sum_{k = 1}^{n} a_{k}^{2}) (\sum_{k = 1}^{n} b_{k}^{2})

source code

 [asciimath]
 --
    ( {\sum_{k=1}^n a_k b_k )\space^{\!\!2 }} \leq
     ( \sum_{k=1}^n a_k^2 ) ( \sum_{k=1}^n b_k^2 )
 --

P (E) = (\binom{n}{k}) p^{k} (1 - p)^{n - k}

source code

 [asciimath]
 --
 P(E) = {n \choose k} p^k (1-p)^{ n-k}
 --