Answer
$\{\frac{10}{9}, 2\}$
Work Step by Step
Step 1. Rewrite the equation as $\sqrt {4x+1}=\sqrt {x-1}+2$
Step 2. Take square on both sides to get: $4x+1=x-1+4\sqrt {x-1}+4$ or $3x-2=4\sqrt {x-1}$
Step 3. Take square on both sides again to get: $9x^2-12x+4=16x-16$ or $9x^2-28x+20=0$ which gives $x=\frac{10}{9}, 2$
Step 4. Check answers in the original equation: they both fit.
