0\\ x-9 > 0\\ (2x-1)(x-9) = 100\\ 2x^2 -x -18x + 9 = 100\\ 2x^2 -19x -91 = 0\\ D = 361 + 728 = 1089\\ x_1 = (19 - 33)/4 = -7/2\\ x_2 = (19+33)/4 = 13\\\\ x = 13" alt="0.5lg(2x-1) + lg\sqrt{x-9}=1\\ lg(2x-1) + 2lg\sqrt{x-9}=1\\ lg(2x-1) + lg(x-9)=2\\ 2x-1 > 0\\ x-9 > 0\\ (2x-1)(x-9) = 100\\ 2x^2 -x -18x + 9 = 100\\ 2x^2 -19x -91 = 0\\ D = 361 + 728 = 1089\\ x_1 = (19 - 33)/4 = -7/2\\ x_2 = (19+33)/4 = 13\\\\ x = 13" align="absmiddle" class="latex-formula">
x_2 = -7/2 не подешел, так как не удовлетворяет ОДЗ