This is a perfect square. First set it equal to 0 by subtracting 25 from both sides
16x^2-25=0
Take the Square root of both terms
Square root of 16x^2 is 4x
Square root of -25 is 5 and -5
The factored form is
(4x+5) (4x-5)
If you set each of these equal to 0 and solve for x you get
4x+5=0
subtract 5
4x=-5
divide by 4
-5/4=x
Do the same with the next factor
4x-5=0
add 5
4x=5
divide by 4
x=5/4
the two roots for this are 5/4 and -5/4