In order to solve this problem we must first complete the square. To complete the square we need to factorise the equation to get the coefficient of x to be 1. This gives: 2(x^2-3x)+5. We then need to complete the square for x^2-3x. This gives: 2((x-1.5)^2-(1.5)^2)+5=2((x-1.5)^2-2.25)+5. [When completing the square we need to half the coefficient of x and minus it from x^2, we then change the x^2 to x and square this. We then minus the value of the coefficient squared from the squared brackets.] We finally need to simplify: 2((x-1.5)^2-2.25)+5=2(x-1.5)^2-4.5+5=2(x-1.5)^2+0.5. So from the initial question this gives a=2, b=1.5, c=-0.5.