48x - 16x^2 > 30 rewrite as
0 > 16x^2 - 48x + 30 rewrite again as
16x^2 - 48x + 30 < 0 divide through by 2
8x^2 - 24x + 15 < 0 set equal to 0
8x^2 - 24x + 15 = 0
Using the quadratic formula, we have
x = [24 ± √[ (-24^2 - 4(8)(15) / [ 2 * 8] =
[ 24 ± √96] / 16 = [ 24 ± 4√6] / 16 = [ 6 ± √6] / 4
We have 3 intervals to test here......either the middle interval works or the two "outside" intervals do
The intervals are (-inf, [6 - √6]/ 4 ) , ( [6 - √6]/ 4, [6 +√6]/ 4 ), ( [6 + √6]/ 4 , inf)
Pick a point in the middle interval - I'll choose 1 - and test it in the original problem
48(1) - 16(1)^2 > 30
32 > 30 this is utrue......thus this interval solves the problem
And the solution is : ( [6 - √6]/ 4, [6 +√6]/ 4 )
