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February 14th, 2017, 10:37 AM   #1
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how to simplify this formula?

How do you simplify this equation to solve for RPM?
6.089/RPM + 1.98RPM = 14,918
It's part of my new formula for determining peak power RPM by transfer port duration and transfer/boost area. (on a 2 stroke engine)
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February 14th, 2017, 10:57 AM   #2
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Multiply by rpm. You will get a quadratic equation.
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February 14th, 2017, 09:31 PM   #3
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First, make it simple by multiplying each term by $1000$

$\dfrac{6089}{\text{RPM}}\;+\;1980\text{RPM}=14918 000$

Now, multiply each term by RPM

$6089\;+\;1980\text{RPM}^2=14918\text{RPM}$

$1980\text{RPM}^2-14918\text{RPM}+6089=0$

We can observe that it's a quadratic equation So, solve it using quadratic formula, i.e.,

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$
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February 15th, 2017, 02:53 AM   #4
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Quote:
Originally Posted by deesuwalka View Post
First, make it simple by multiplying each term by $1000$

$\dfrac{6089}{\text{RPM}}\;+\;1980\text{RPM}=14918 000$

Now, multiply each term by RPM

$6089\;+\;1980\text{RPM}^2=\color{red}{14918000RPM }$
$\color{red}{correction}$
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February 15th, 2017, 06:40 AM   #5
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Quote:
Originally Posted by jaguar57 View Post
6.089/RPM + 1.98RPM = 14,918
x = RPM; rewrite after multiplication by 1000:
6089/x + 1980x = 14918000
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