Math problem please help?

Common difference of the geometric sequence :
(2x - 14)/(x - 1) = 3x/(2x - 14)
(2x - 14)² = 3x(x - 1)
4x² - 56x + 196 = 3x² - 3x
x² - 53x + 196 = 0
(x - 4)(x - 49) = 0
x = 4 or x = 49

3x/(2x-14) = (2x-14)/(x-1)
3x(x-1) = (2x-14)²
3x²-3x = 4x²-56x+196
x² - 53x + 196 = 0

quadratic formula
x = [53 ± √(53² – 4·1·196)] / [2·1]
 = [53 ± √2025] / 2
 = [53 ± 45] /2
 = 49, 4

(2x - 14)/(x - 1) = 3x/(2x - 14)
(2x - 14) (2x - 14) = (3x)(x - 1)
4x² - 56x + 196 = 3x² - 3x
x² - 53x + 196 = 0
( x - 49 ) ( x - 4 ) = 0
x = 4 , x = 49

　
a, b, c is in geometric sequence if there is a common ratio between consecutive terms:
r = b/a = c/b

Geometric sequence: x−1, 2x−14, 3x

(2x−14)/(x−1) = 3x/(2x−14)
(2x−14)² = 3x(x−1)
4x² − 56x + 196 = 3x2 − 3x
x² − 53x + 196 = 0
(x − 4) (x − 49) = 0
x = 4, x = 49

x = 4 ----> Geometric sequence: 3, −6, 12 (r = −2)
x = 49 ----> Geometric sequence: 48, 84, 147 (r = 7/4)

Geometric sequences have this as a general form for the "n"th term of the sequence:

a(n) = ab^(n - 1)

where "a" is the first term and "b" is the common ratio.

So if your first three terms are:

x-1; 2x-14; 3x

Then we can say:

a = x - 1

So substituting this expression for "a", and n = 2, we can derive an expression for b:

a(n) = ab^(n - 1)
2x - 14 = (x - 1)b^(2 - 1)
2x - 14 = (x - 1)b^(1)
2x - 14 = (x - 1)b
b = (2x - 14) / (x - 1)

And then we can do the same for n = 3, having an expression for a and b now:

a(n) = ab^(n - 1)
3x = (x - 1)[(2x - 14) / (x - 1)]^(3 - 1)
3x = (x - 1)[(2x - 14) / (x - 1)]^(2)
3x = (x - 1)(2x - 14)² / (x - 1)²

One (x - 1) cancels out with the (x - 1) from the value of "a":

3x = (2x - 14)² / (x - 1)

Now let's multiply both sides by (x - 1), then expand both halves:

3x(x - 1) = (2x - 14)²
3x² - 3x = 4x² - 56x + 196
0 = x² - 53x + 196

This factors:

0 = (x - 4)(x - 49)

so we get:

x = 4 and 49

There are two values for x that makes this work.

(2x - 14)/(x - 1) = 3x/(2x - 14) =>
4(x - 7)^2 = 3x*(x-1) =>
4x^2 - 56x + 196 = 3x^2 - 3x =>
x^2 - 53x + 196 = 0 =>
(x - 4)(x - 49) = 0 => x = 4 or x = 49.

Check:
3, -6, 12 are in geometric series with common ratio -2 (negative 2).
48, 84, 147 are in geometric series with common ratio 7/4 (or 1.75).

i cant