Solve for the largest value of $x$ such that $5(9x^2+9x+10) = x(9x-40).$ Express your answer as a simplified common fraction.

Hello, please consider the following.

We can estimate the discriminant, and then, the solutions and we take the largest one.

Thank you

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.