Solve \[\sqrt{4x+13}-\sqrt{x+1}=\sqrt{12-x}.\]

One root of the equation \[3x^3+14x^2+2x-4=0\] is rational. Obtain this root and complete the solution of the equation.

Solve \[\sqrt{4x+13}-\sqrt{x+1}=\sqrt{12-x}.\]

One root of the equation \[3x^3+14x^2+2x-4=0\] is rational. Obtain this root and complete the solution of the equation.