94x: Fill & Download for Free

[math]3x^2=94x+6\\\text{subtrac}\;94x+6 \;\;\text{from both sides}\\\Rightarrow 3x^2-94x-6=94x+6-94x-6\\\Rightarrow 3x^2-94x-6=0\\\text{Now, we can observe that it's a quadratic equation so, solve it using quadratic formula. i.e.,} \\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\text{Here,} a=3,\;\;b=-94,\;\;c=-6\\x=\dfrac{94\pm\sqrt{(-94)^2-4(3)(-6)}}{2(3)}\\=\dfrac{94\pm\sqrt{8836+72}}{6}\\=\dfrac{94\pm\sqrt{8908}}{6}\\=\dfrac{94\pm\sqrt{4×2227}}{6}\\=\dfrac{94\pm2\sqrt{2227}}{6}\\x=\dfrac{47}{3}-\dfrac{\sqrt{2227}}{3}\\x=\dfrac{47}{3}+\dfrac{\sqrt{2227}}{3}\tag*{}[/math]

Not really.The relationship between engine size and efficiency is not linear. It's more like a parabola. There comes a point in size where the engine stops getting more efficient the bigger it gets. That point is about 4m in diameter. The most powerful turbofan engine in history is the GE90 with 115,000lbs of thrust and it has a fan diameter of 3.3m.Which as you can see……is already big enough. Though there's still room for some expansion.The future of jet engine development does not lie in increasing the size, but in introducing more clever technologies.One such technology is the geared turbofan. As you probably know, turbofan engines are turbojet engines coupled to a large, shrouded fan. One of the inefficiencies of this coupling is that the core of the engine’s efficiency range is different from the fan’s. The fan needs to spin slower for best performance to keep the tips from nearing supersonic flow, while the core needs to spin faster to produce more power. The solution to that is a reduction gear system that connects one to the other, allowing both the compressor and the fan to spin at their most efficient speeds. This is a technology 30 years in the making and the first one to power airliners will be the PW1000G, with %16 reduced fuel consumption according to Pratt & Whitney. Another one in development is Rolls-Royce’s Trent Ultrafan, which can also have a variable pitch fan.The other is the propfan (also called open-rotor engine or unducted fan). This design takes the large spinny bit of the turbofan engine, multiplies it by two (contra-rotating) and puts it outside the engine, resulting in over %30 reduced fuel consumption near conventional turbofan engine cruise speeds. This has also been in the making for many decades (40 years). In the late ’80s, McDonnell Douglas tested a propfan design on one of their MD-80s and were satisfied with the results enough that they started development on the MD-94X, a propfan powered airliner based on the MD-80. Decreasing fuel prices has resulted in waned interest however and apart from a few concept designs and the Progress D-27 engine, it's been mostly unexplored.However, with fuel costs rising yet again, the interest in propfans is growing and there's a possibility that the next generation of airliners might be offered with these engines. Airbus has already patented one such desig. Currently the only aircraft with propfan engines in active service is the Antonov An-70.Oh and since you mentioned high-bypass engines, I'm assuming you are aware that increasing the bypass ratio equals greater efficiency/power. Well, you might be interested to learn that one of the names used for propfans is “ultra high-bypass” engine.

Assuming x2 means x squared there is no solution.Taking just the first identity:3x^2=94x+63x^260x^2+94x=0x(60x+94)=0x=0 or x=-94/60Now substituting x=0 yields 0 = 0 = 1 = 7 which is false.And substituting x=-94/60 also yields a falsehood.So there is no solution.But I guess there probaby is some typo, as in the right equations x^2 is written properly, so maybe you mean something else?