Tricky Math Problem!

Ok, well today I had my end of course exams in Algebra one. While I was doing the test I found this question (I'll give the gist of it; the non gardening-fence-patio version) It's a pythagorean theorem/ factoring problem:

Basically there is a right triangle; the hypotenuse is 18 and the sides are X and (X+3)

I'll "paint" a picture if its necessary (not really necessary right? whatever) Imagine a square the diagonal going from the top left corner to the bottom right; then dock the bottom left part (and it didn't even take a thousand words! :D) As said, the hypotenuse is 18, the top leg is X and the other leg is (X+3).

I get the whole factoring thing and stuff but I hit a lot of road blocks that made me resort to trial and error by plugging in numbers logically (I first established which numbers it was between and went on into the decimals). Can you help and please show your work? I'll edit with my answer later.

Edit: added more steps, plus corrected a sign error.

x^2 + x^2 + 6x + 9 = 324
2x^2 + 6x - 315 = 0
x^2 + 3x = 315/2
x^2 + 3x + 9/4 = 315/2 + 9/4
(x + 3/2)^2 = 639/4
x + 3/2 = ± √639 / 2
x = -3/2 ± (3√71) / 2
x = 3/2(-1 ± √71) => reject the negative
x = 3/2(-1 + √71)
x ≈ 11.14

You are welcome, and thanks for the BA.

Regards.

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Do you have to find the x or something?

If so.. then this is what you know:
A = x
B = (x+3)
C = 18

A²+B²=C²

18² - x² = (x+3)²

18² - x² = x²+6x+9

2x²+6x-315

now with the ABC-formula (not the same as ABC from the triangle)

A=2
B=6
C=-315

X1,2 = (-6+/- sqrt(6²-4*2*-315)) / (2*2) = 11.139 or - 14.139
the -14,139 isn't really a value you can plug into a side of a triangle. The real answer is x=11.139