Как решить lg(x-5)-lg корень из разности 5x-10=0

The UK consists of 4 parts.The Republic of Ireland governs most of the island of IrelandThe UK is divided into countries.In the UK lawyers rely mostly on parliamentary laws.The British government comprises three powers.The UK has a queen as its Head of State.The local government is situated in a county town.The UK Constitution includes several constituents.The UK covers about 244,000 square kilometers, "The United Kingdom of Great Britain and Northern Ireland" is the official name of the Great Britain.

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[latex]lg(x-5)-lg sqrt{5x-10}=0 [/latex]ОДЗ:[latex] left { {{x-5 extgreater 0} atop {5x-10 extgreater 0}} ight. Rightarrow left { {{x extgreater 5} atop {x extgreater 2}} ight. [/latex]x∈(5;+∞)[latex]lg frac{x-5}{ sqrt{5x-10} }=0 \ \ frac{x-5}{ sqrt{5x-10} }=1 \ \ x-5= sqrt{5x-10} \ \ x^2-10x+25=5x-10 [/latex]x²-15x+35=0D=225-140=85x=(15+√85)/2    или     х=(15-√85)/2<5 и поэтому не входит в ОДЗОтвет.x=(15+√85)/2