Lifetime earnings calculation doesn't work

I tried to solve for how much money I need to get 100 angel investors using this formula:

150 * sqrt(x/1 quadrillion) = 100

where x = earth lifetime earnings

However this gives me 4 + 4/9 quadrillion for x, which obviously isn't right since 1 quadrillion gives you 150 angel investors.

Here is how I calculated it:

1) divide by 150 to isolate the square root
2) Square both sides
3) multiply by 1 quadrillion

This gives me x by itself but obviously something is wrong because I only need a fraction of a quadrillion to get 100 angel investors, not 4 + 4/9 quadrillion(which in the game would show up as 4.444 quadrillion).

I tried wolfram alpha but it gives me the same wrong result.

So why doesn't my calculation work for solving for the lifetime earnings for a given number of angel investors(at least below 150 it doesn't work)?

Your math is very spot on

I myself have calculated this and found that AC has counters that fluctuate depending on what you do

I found this out by using Cheat Engine on a fresh, new game save to see what the price was (Your math was spot on for fresh saves) vs my save I had for 2 years

So the difference was that the fresh save, since nothing was completed and no money was generated besides the Cheat Engine changing the values for the money, it has the base value


Now the more progressed save had a harder time achieveing 150 Angels and of course, the save was also reset multiple times so that I can get my earned angels

Now looking into the files, doing my research and making sure that nothing was left out afterwards, I have the final informtion piece. With every reset the money range increases (As stated in the files using a very professional software) meaning the money needed to recieve 150 Angels doubles the average cost.

Here is the data I observed

Lifetime Earnings ($) Angel Investors Lifetime Earnings ($) Angel Investors
Ten (10) 0 Quadrillion (1015) 150
Hundred (100) 0 Quintillion (1018) 4,743
Thousand (1000) 0 Sextillion (1021) 150,000
Million (106) 0 Septillion (1024) 4,743,416
Billion (109) 0 Octillion (1027) 150,000,000
≈ 45 Billion 1 Nonillion (1030) 4,743,416,490
Trillion (1012) 4 Novemvigintillion (1090) 4,74 × 1039

Here are the simplest tests and math I can do to make sure that your answers are answered
The top one is the answered one for 150 Angels and the bottom one is the maxed out Angel Investor limit

This chart I have created is only regarding fresh new saves and leaving the more complicated save out. If there is any miscalculation in my math please tell me