Answer
$x=\frac{3}{4}$
Work Step by Step
$2x=\sqrt {-5x+24} -3$
$2x+3=\sqrt {-5x+24}$
Squaring both sides of the equation..
$4x^2+12x+9=-5x+24$
$4x^2+17x-15=0$
$4x^2+20x-3x-15=0$
$4x(x+5)-3(x+5)=0$
$(4x-3)(x+5)=0$
$x=-5$
$x=\frac{3}{4}$
Check:
For $x=\frac{3}{4}$
$\frac{3}{2}=\sqrt {\frac{81}{4}} -3, \frac{3}{2}=\frac{3}{2}\checkmark$
For $x=-5$
$-10=\sqrt {49}-3,-10=7-3,-10=4$ Thus, $x=-5$ is an extraneous solution to the equation.
The solution of the given equation is $x=\frac{3}{4}$.
