The number of real solutions of the equation (9/10)x=−3+x−x2 is

Let f(x)=−3+x−x2. Then f(x)< 0 for all x, because coefficient of x2 is negative and D < 0. Thus, L.H.S. of the given equation is always positive, whereas the R"H.S. is always less than zero. Hence, there is no solution.