Cho phương trình left( 1,5 right)x2 - x - 5 = left( frac23 right)2x + 3. Gọi

Ta có
${\left( {1,5} \right)^{{x^2} - x - 5}} = {\left( {\frac{2}{3}} \right)^{2x + 3}} \Leftrightarrow {\left( {\frac{3}{2}} \right)^{{x^2} - x - 5}} = {\left( {\frac{2}{3}} \right)^{2x + 3}} \Leftrightarrow {x^2} - x - 5 = - 2x - 3 \Leftrightarrow {x^2} + x - 2 = 0 \Leftrightarrow \left[ \begin{array}{l} {x_1} = - 2\\ {x_2} = 1 \end{array} \right..$
Khi đó $A = {x_1} - 2{x_2} = - 2 - 2.1 = - 4.$