A possibly better solution to this problem, given that it may not always be multiple choice, is to actually find the zeroes of this function.
First you would let f(x)=-8x^2+4x+7=0
Now, since you were asked for an approximate answer, and this is a quadratic equation, you can use the quadratic formula, which says that the roots (the zeroes) of a function of this type (ax^2+bx+c=0) are equal to:
Plugging in a=-8, b=4 and c=7 simplifies to
Plugging these into our calculators gives the last solution set.
You may also be familiar with factoring quadratic equations into the form (x-n)(x-m)=0 in order to solve them. With this one, a hint that you should use the quadratic equation is that the constant term (c or 7 in this problem) is prime, that is there are no integers that you can multiply together to get seven