find a quadratic equation with solutions 3 and(-5/2)

+3 and -5/2 are the roots of the equation.

this means that the quadratic equation has factors

(x-3)((x+5/2) = 0

relatively straightforward to FOIL thes binomial factors to get

x^2 + (5/2 x - 3x) -15/2 = 0

combine like terms (in the parentheses) to get

x^2 -(1/2)x -15/2 = 0