Factorise:

The given expression is $2 x^{2}+x-45$.

Find two numbers that follow the conditions given below:

Sum $=1$

Product $=-45 \times 2=-90$

Clearly, the numbers are 10 and $-9$.

$2 x^{2}+x-45=2 x^{2}+10 x-9 x-45$

$=2 x(x+5)-9(x+5)$

$=(2 x-9)(x+5)$