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# Any help will be appreciated with this problem. Thanks!

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Find the largest possible value of $$x$$ in the simplified form $$x = {a \pm b\sqrt{c} \over d}$$ if $$\frac{5x}{6} + 1 = \frac{3}{x}$$ where $$a, b, c,$$ and $$d$$ are integers. What is $$\frac{acd}{b}$$

Oct 16, 2020

#1
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Multipl through by x to get

5x^2 /6 + x = 3    Multiply through by 6

5x2 + 6x - 18 = 0     Quadratic Formula shows answers   as  ( 3 +- 3 sqrt 11 ) / 5         ..... you can finish the answer from here .....

Oct 16, 2020
#2
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Oops! Just realized I made a little typo. It's supposed to be $$x = {a + b\sqrt{c} \over d}$$

Oct 16, 2020
#3
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Thanks ElectricPavlov! You were correct, and now I understand!

Oct 16, 2020
#4
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You're welcome !

ElectricPavlov  Oct 16, 2020