Answer
$$x=\frac{1}{2}, -\frac{5}{9}$$
Work Step by Step
Solving the equation for x, we find:
$$9x\left(2x-1\right)+5\left(2x-1\right) \\ \left(2x-1\right)\left(9x+5\right) \\ x=\frac{1}{2}, -\frac{5}{9}$$
Checking this solution by plugging it back in, we find that the solution is correct.