To solve this equation, we can simplify each side separately and then compare the results.

On the left side:
172x^2 - 7^9 = 172x^2 - 7^(2*3) = 172x^2 - 7^6

On the right side:
98^3 = (2*7)^3 = 2^3 * 7^3 = 8 * 343 = 2744

So the equation becomes:
172x^2 - 7^6 = 2^-3

Now, let's simplify the right side:
2^-3 = 1/2^3 = 1/8

Now we have:
172x^2 - 7^6 = 1/8

To solve for x, we need to isolate the variable. Let's multiply both sides by 8 to get rid of the fraction:
8 * (172x^2 - 7^6) = 8 * (1/8)
1376x^2 - 8 * 7^6 = 1

1376x^2 - 8 * 117649 = 1

1376x^2 - 941192 = 1

1376x^2 = 941193

Now, divide both sides by 1376 to solve for x:
x^2 = 941193/1376

x^2 ≈ 683.5

Taking the square root of both sides:
x ≈ ±26.15

So the approximate solutions for x are x ≈ 26.15 and x ≈ -26.15.