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Whats the simplest way to solve this? $12b-\frac{b^2}{2} = 36$

I am trying to find $b$ where the the line $x=b$ divides a region into two equal parts of equal area. The integral is $\int_{0}^{12}(12-x)~dx = 72$ so $\int_{0}^{b}(12-x)~dx=36$. I believe I set this up correctly, if not how do I solve for $b$?

Thanks

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    That is a quadratic equation you have. – 2017-01-29
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    The simplest way is to ask someone else to answer it for you. – 2017-01-29
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    Thank you so much Oppa for your extremely insightful answer. – 2017-01-29

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multiplying by $2$ and rearranging we get $$0=b^2-24b+72$$ using the quadratic formula we get $$b_{1,2}=12\pm\sqrt{144-72}$$ can you proceed?

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    $b=12-\sqrt{144-72}$ thanks – 2017-01-29
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    and the other solution? – 2017-01-29
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    Well the other solution is $b=12+\sqrt{144-72}$, but that wouldn't work right? Since I am looking for a number between $0$ and $12$. – 2017-01-29
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    ok then is all to the best – 2017-01-29
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    yes i have it known yet – 2017-01-29
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    you are welcome – 2017-01-29
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    I have one more question. How did you get $12\pm\sqrt{144-72}$ from $\frac{24\pm\sqrt{288}}{2}$? – 2017-01-29