y=4x^2 + 6x - 2

Jimmy,

The number of answers in infinite, as the value of X will depend on Y. As an example, let's say Y were equal to 7 (just because). If Y were equal to 7, I would therefore have:

7 = 4x^{2} + 6x - 2.

Now remember, the quadratic formula only works if the equation IS SET EQUAL TO ZERO. So the first thing I have to do is subtract 7 from each side:

0 = 4x^{2} + 6x - 9 Hopefully, that makes sense. It's just a little bit of algebra. Now I can use the quadratic formula where A = 4, B = 6 and C = -9.

Remember the quadratic formula:

With that in mind, let's plug and chug! -6 + sqrt[36 - 4(4)(-9)]...all divided by 2(4)

That rounds out to -6 + squrt(180) all divided by 8.

The simplest that gets is -3 + 3sqrt(5) all divided by 4.

That's just if y is 7. Remember, always set it to zero.