Answer
$-3,1$.
Work Step by Step
Step 1. Rewrite the equation as $\sqrt {-2x+3}=3-\sqrt {x+3}$
Step 2. Take square on both sides to get $-2x+3=9-6\sqrt {x+3}+x+3\longrightarrow 6\sqrt {x+3}=3x+9 \longrightarrow 2\sqrt {x+3}=x+3$
Step 3. Take square on both sides again to get $4(x+3)=x^2+6x+9 \longrightarrow x^2+2x-3=0$
Step 4. Factor the equation to get $(x+3)(x-1)=0$, we have $x=-3$ and $x=1$
Step 5. Check the above answers and we find that they both fit the original equation, thus the solutions are $x=-3$ and $x=1$.
