# Solving an equation for k_t in a modified Solow model

I want to solve my modified solow equation for k_t to get the steady state. But since I also inclueded the marginal product for the price of Energy its pretty difficult for me to find a solution.

here is the equation

$$\frac{\delta \cdot k_t}{s \cdot A \cdot k_t^\alpha} = \left(\frac{P_e}{\gamma \cdot A \cdot k_t^\alpha}\right)^{\frac{\gamma}{\gamma-1}}$$

I want to solve for $$k_t$$

Here is the initial equation.

$$0 = s \cdot A \cdot k_t^\alpha \cdot \left(\frac{P_e}{\gamma \cdot A \cdot k_t^\alpha}\right)^{\frac{\gamma}{\gamma-1}} - \delta \cdot k_t$$

I would be really thankful if someone could help me or give me a hint

$$\begin{eqnarray} \frac{\delta \cdot k_t}{s \cdot A \cdot k_t^\alpha} & = & \left(\frac{P_e}{\gamma \cdot A \cdot k_t^\alpha}\right)^{\frac{\gamma}{\gamma-1}} \\ \frac{\delta}{s \cdot A} \cdot k_t^{1-\alpha} & = & \left(\frac{P_e}{\gamma \cdot A}\right)^{\frac{\gamma}{\gamma-1}} \cdot k_t^{-\frac{\gamma}{\gamma-1}\alpha} \\ k_t^{1-\alpha} \cdot k_t^{\frac{\gamma}{\gamma-1}\alpha} & = & \frac{s \cdot A}{\delta} \cdot \left(\frac{P_e}{\gamma \cdot A}\right)^{\frac{\gamma}{\gamma-1}} \\ k_t^{1-\frac{\alpha}{\gamma-1}} & = & \frac{s \cdot A}{\delta} \cdot \left(\frac{P_e}{\gamma \cdot A}\right)^{\frac{\gamma}{\gamma-1}} \end{eqnarray}$$ And then you just substitute the parameters and take the right hand side to the proper power.