will my 460w power supply run a 270x?

Solution
A R9 270x needs 24A on the 12V rail and a total of at least 500W for the whole pc.

But unless its a good brand, you'll be inviting an expensive disaster. Get one from Tier One -http://www.tomshardware.com/answers/id-1804779/power-supply-unit-tier-list.html#13224310

http://www.gigabyte.com/products/product-page.aspx?pid=4795#sp

Unlikely.
The recommended minimum is 500W but with two, 6-pin Graphic connectors. The general rule of thumb for picking a Power Supply when you have a video card is to ensure it has the proper of 6-pin and/or 8-pin graphic connectors. If that's the case you're likely fine.

In your case you MAY get if you have one already and add a 6-pin MOLEX adapter but I strongly recommend it. I recommend a 600W or 650W with the proper connectors.
 
A R9 270x needs 24A on the 12V rail and a total of at least 500W for the whole pc.

But unless its a good brand, you'll be inviting an expensive disaster. Get one from Tier One -http://www.tomshardware.com/answers/id-1804779/power-supply-unit-tier-list.html#13224310
 
Solution
A Radeon R9-270X needs at least 24 amps on the 12v rail and a 500 watt power supply.Both units below meet the criteria.

Don't skimp on the power supply it's the heart of your system , this is the Best deal on the market.

This power supply is OEM sized , the exact same size as the 460 watt in your tower.
Dimensions: 150mm x 140mm x 86mm (5.9 x 5.5 x 3.4 inches)

It will give you more than enough power for the 270x.
It has 45 amps on the 12v rail.
Made by the best = SEASONIC.


PCPartPicker part list / Price breakdown by merchant / Benchmarks

Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($47.99 @ NCIX US)
Total: $47.99
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-05-08 22:50 EDT-0400)

If you are on a strict budget this is a solid choice , but I recommend the XFX 550W just above this one.

PCPartPicker part list / Price breakdown by merchant / Benchmarks

Power Supply: EVGA 500W 80+ Bronze Certified ATX Power Supply ($34.99 @ Micro Center)
Total: $34.99
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-05-08 23:01 EDT-0400)

This one is the Best 550w on the market.

Gold Certified \ Full modular


PCPartPicker part list / Price breakdown by merchant / Benchmarks

Power Supply: XFX XTR 550W 80+ Gold Certified Fully-Modular ATX Power Supply ($89.99 @ Newegg)
Total: $89.99
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-05-08 23:08 EDT-0400)
 
This is my recommended R9-270X (Asus). It seems to have good reviews. I wouldn't spend much more anyway or then I'd be recommending the Asus or EVGA GTX760 instead.
http://pcpartpicker.com/part/asus-video-card-r9270xdc2t2gd5

For Power Supplies, I'll give a list of several and recommend you research them a bit more (customer comments, and reviews if you can find them.)

There are three kinds:
1) Non-Modular,
2) Semi-Modular, and
3) Full Modular

I prefer Semi-Modular. The main wires are soldered in permanently which everyone uses anyway, but the other wires can be inserted as needed to reduce clutter. However, my FIRST priority is based on the QUALITY of it so it doesn't die or damage other components (get a surge protector as well. A well-made $30 one is okay.)

A suitable 500W is "good enough" but for the small price difference I recommend 600W or better. For longevity, and fan noise as well since most fans start ramping up at 50% load (250W).

List of PSU's (600W+):

http://pcpartpicker.com/part/evga-power-supply-100b10600kr

http://pcpartpicker.com/part/ocz-power-supply-oczzt650w

http://pcpartpicker.com/part/corsair-power-supply-cx600

http://pcpartpicker.com/part/antec-power-supply-neoeco620c

http://pcpartpicker.com/part/corsair-power-supply-cx600m

http://pcpartpicker.com/part/silverstone-power-supply-st60fes
 
The 550W one linked above my comment seems adequate. The only reason you may wish to avoid it would be if you want Semi or Fully-Modular to avoid excess wires but it appears pretty good.

Here's the wire breakdown (has 1x6-pin, and 1x6/8-pin so supports): http://www.jonnyguru.com/modules.php?name=NDReviews&op=Story&reid=225

Other:
If you have a stock or crappy fan (which many pre-builts do) you may want to replace it with a Cooler Master Hyper 212 EVO. That's solely about NOISE not cooling.
 
http://www.techpowerup.com/reviews/ASUS/R9_270X_Direct_Cu_II_TOP/24.html

POWER and FAN NOISE:
Based on your computer motherboard's max CPU TDP capability I estimate your maximum power consumption with a R9-270X would be 300W which works out to about 54% load of a GTX550W PSU.

Thus the 550W linked by SR-71 Blackbird put you right about the recommended power level (50 to 60%). Again, fan noise tends to ramp up past 50% so for price, fan noise, and quality this is pretty good. The only issue is the Modular one but frankly I don't think there's too much cable excess nor will you even see it.

I should add that there may be an issue with improper connections on some of the Modular power supplies, which isn't an issue when they are soldered in.