what is the minimum for this equation

what is the minimum for this equation, C(x) 0.5x^2+23x-216+2600/x

Minimum c'(x) = 0

$$c'(x) = 2 * 0.5 x +23 -1*(2600)x^{-2}=x +23 -\frac{2600}{x^{2}} = 0\\ c'(x) = 0:\\ x +23 -\frac{2600}{x^{2}} = 0\\ \frac{2600}{x^{2}} = x+23\\ 2600 = x^2(x+23)\\ 2600 = x^3+23x^2\\ x^3+23x^2-2600=0\\ x= 9.01217 ( \mbox{ and 2 imaginary solutions} )$$

c(9.01217) = 320.38829

Minimum: (9.01217, 320.38829)