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sqrt(10^8+10^12/(x))/sqrt(9*10^8+(10^12)/x)=(1/sqrt(2)) equation

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Numerical solution:

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The solution

You have entered [src]
    ___________________________        
   /             1000000000000         
  /  100000000 + -------------         
\/                     x            1  
------------------------------- = -----
    ___________________________     ___
   /             1000000000000    \/ 2 
  /  900000000 + -------------         
\/                     x               
$$\frac{\sqrt{100000000 + \frac{1000000000000}{x}}}{\sqrt{900000000 + \frac{1000000000000}{x}}} = \frac{1}{\sqrt{2}}$$
The graph
Sum and product of roots [src]
sum
10000/7
$$\frac{10000}{7}$$
=
10000/7
$$\frac{10000}{7}$$
product
10000/7
$$\frac{10000}{7}$$
=
10000/7
$$\frac{10000}{7}$$
10000/7
Rapid solution [src]
x1 = 10000/7
$$x_{1} = \frac{10000}{7}$$
x1 = 10000/7
Numerical answer [src]
x1 = 1428.57142857143
x1 = 1428.57142857143