How to solve an equation with a decimal exponent? Forgive me but I don't know the formal term for the type of equation I am talking about, but it is of the form:
$$Ax^n + Bx^2 + Cx + D = 0$$
where $A$, $B$, $C$ and $D$ are constants and $n$ is some decimal number such as $2.3256 \ldots$, etc.
In general is such an expression solvable? 
Thanks,
 A: No, according to Galois theory, only linear, quadratic, cubic and quartic equations can be solved in general. 
It is not meant that none of equations excluding the type mentioned above, are solvable. For example, equations like $ax^{2n}+bx^n+c=0 $, or the equation $x^{1/2}-x^2=1$ is solvable.
A: If the exponent $n$ can be written ( as reduced fraction) $n=\frac{p}{q}$, then reordering and taking the $q-$power your equation can be writtenas:
$A^qx^p=(-Bx^2-Cx-D)^q$.
This is a polynomial equation whose solubility is regutated by the Abel-Ruffini theorem. This means that, in general, we don't have a solution in radical form if the degree of the equation (that is the gratest value from $p$ and $2q$) is $\ge 4$. But for some special values of $A,B,C,D$ some solution can exist that can be espresssed by radicals.
Furthermore, whan we take the  $q-$power, if $q$ is an even number, we introduce also the solutions of the equation: $A^qx^q=(Bx^2+Cx+D)^q$, so we have to verify the validity of any algebraic solution.
In conclusion, the best way to solve an equation of the given form, is to use some numerical method as suggested in the comments.
