Do not use a calculator in this question.

(a) Show that

\(\sqrt{24}\times\sqrt{27}+\frac{9\sqrt{30}}{\sqrt{15}}\)

can be written in the form \(a\sqrt2\), where \(a\) is an integer.

(b) Solve the equation \(\sqrt3(1+x)=2(x-3)\), giving your answer in the form \(b+c\sqrt3\), where \(b\) and \(c\) are integers.