Log2 (2x+1)=2log2 3-log2 (x-4)

$log_2(2x+1)=2log_23-log_2(x-4);$
ОДЗ:

0} \atop {x-4>0}} \right. \Rightarrow \left \{ {{x>-\frac{1}{2} } \atop {x>4}} \right. " alt=" \left \{ {{2x+1>0} \atop {x-4>0}} \right. \Rightarrow \left \{ {{x>-\frac{1}{2} } \atop {x>4}} \right. " align="absmiddle" class="latex-formula">

4" alt=" \Rightarrow x>4" align="absmiddle" class="latex-formula">
$log_2(2x+1)+log_2(x-4)=log_29;$
$log_2(2x+1)(x-4)=log_29;$
$(2x+1)(x-4)=9;$
$(2x+1)(x-4)=9;2 x^{2}-7x-13=0;D=49+104=153;$
$x_1= \frac{7- \sqrt{153}}{4};$ посторонний корень
$x_2= \frac{7+ \sqrt{153}}{4};$
Ответ: $x= \frac{7+ \sqrt{153}}{4}$