Solve the following quadratic equation: 2x^2 - 5x - 3 = 0

Firstly, we need to factorise the equation:We can see (and are told) that the equation is quadratic and is therefore of the form ax^2 + bx + c. In our case, a=2, b=-5 and c=-3. We therefore expect two pairs of brackets that look like: (?x + ?)(?x + ?).We are looking for two numbers that multiply to give a. One obvious choice is 2 and 1. We then have (2x + d)(x + e). We now need to find the two unknown numbers that give the correct values for b and c: 2xe + xd = b = -5x and de = c = -3. The second equation is solved using d, e = 1, -3 or 3, -1. We see which of these satisfies the first additional equation as well.Try d = -3, e = 1: 2x1 + x*-3 = 2x - 3x = -1x. This does NOT solve the equation.Try d = 1, e = -3: 2x*-3 + x*1 = -6x + x = -5x. This does solve the equation.The factorised equation is: (2x + 1)(x - 3) = 0 and the solutions are x=-1/2 and x = 3.