What's the answer
It would be easier to just factor since this polynomial is a perfect square, but since your teacher is asking you to use the quadratic formula, we'd better do that too:
y = ax2 + bx + c
y = x^2 - 3x + 9/4
a = 1, b = -3, c = 9/4
The quadratic formula gives you the values of x when y = 0:
x = (-b + or - square root (b^2-4ac)) / 2a
x = (3 + or - square root (9 - 9)) / 2
x = (3 + sqrt(0) )/ 2 ; (3 - sqrt(0) )/ 2
x = 3/2
You can use factoring or completing the square to check your answer, or graph it on your calculator to double check your answer.
Hope this helps!