Question

5x2+9x-2=0

Answer 1

You must factor the left side first.
5x^2 = (5x)(x), so you'll have
(5x )(x )
Now you need two numbers that multiply to -2: -1 and 2 or 1 and -2
Now there are 4 possibilities as to where those numbers go:
(5x - 1)(x + 2)
(5x + 2)(x - 1)
(5x + 1)(x - 2)
(5x - 2)(x + 1)
To choose the right one, do OI of FOIL with each one of the 4 possibilities above and add the results together and see which one gives you the middle term you have, +9x

For example, if you try the first one, OI will be 5x(2) - 1(x) = 9x
Since 9x is what you need, the first one is it, so
5x^2 + 9x - 2 = 0
(5x - 1)(x + 2) = 0
5x - 1 = 0 or x + 2 = 0
5x = 1 or x = -2
x = 1/5 or x = -2