Question 1 Consider a closed economy, in which the per worker production function is y=Ak^0.5. Suppose that there are transaction costs taking the form of legal fees. The parameter b measures the per worker transaction costs of converting savings into investment. In addition, suppose that two First Nations Reserves (FNRs) share the following parameters: A=4 ,s=10%,n=6%,b=30% and d=4%. One of the FNR them is in the low-income steady state equilibrium and the other FNR is in the high-income steady state equilibrium.

b) Solve for the steady state capital per worker for each of the two equilibria. Substitute the production function into the equilibrium condition sAk 0.5 - b=(n+d) k and then the parameter values 0.1 k - 0.4 k^0.5+0.3=0. You may find the roots in the following manner: 0.1 k - 0.1 k 0.50.3 k 0.5+0.3=0. By multiplying by 10 both sides k - k^0.53 k^0.5+3=0 and collecting terms, we determine that (k^0.53)(k^0.51)=0. This yields the values of the two steady states: k L =1 and k H =9.

Explain the math behind part b, I don't understand.