Verified answer

[tex]\displaystyle\bf\\x^{3} -5x^{2}+9x-45=0\\\\(x^{3} -5x^{2})+(9x-45)=0\\\\x^{2} \cdot(x-5)+9\cdot(x-5)=0\\\\(x-5)\cdot(x^{2} +9)=0\\\\x^{2} +9\neq 0 \ \ \ \Rightarrow \ \ \ x-5=0 \ \ \ \Rightarrow \ \ \ x=5\\\\Otvet \ : \ 5[/tex]