How do I solve this math problem?

Case 1 : The equation is h² + 12740"h" = 20000000

h² + 12740h = 20000000
h² + 12740h - 20000000 = 0
It is a quadratic in the form of ax² + bx + c = 0
where a = 1, b = 12740, c = -20000000

h = [-b ± √(b² - 4ac)] / (2a)
h = [-12740 ± √(12740² + 4*1*20000000)] / 2
h = 1413 or x = -14153 (rejected)

Hence, the height = 1413 km


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Case 2 : The equation is h² + 12740 = 20000000 as stated in the question

h² + 12740 = 20000000
h² = 19987260
h = 4471 or h = -4471 (rejected)

Hence, the height = 4471 km

h^2 + 12740 h = 20000000
h^2 + 12740 h - 20000000 = 0
(h + 6370)^2 - 60576900 = 0
Solutions:
h
= -10 (637 + sqrt(605769))
Negative value to be ignored.
h
= 10 (sqrt(605769) - 637)
≈ 1413.1

This is a two step equation:

h² + 12740 = 20000000

First subtract the 12740 from both sides so the h² term is by itself:

h² = 19987260

Now get the square root of both sides. You are told to only look at the positive result, so we'll throw the negative one away:

h = 4471 (rounded to the nearest whole)

So I don't get what you say you should get. So either the question or your answer is wrong.

If the problem is 2,000,000 instead of 20,000,000, we get this:

h² + 12740 = 2000000
h² = 1987260
h = 1410 km (rounded to nearest whole), which is closer to what you say you should get, but still not exact.

h² + 12740 = 20000000
h² = 19987260
h = 4471 km

if you made a typ0 and it should be
h² + 12740 = 2000000
h = 1410 km
closer