Where is the mistake in that equation

(x²-14)²=5(6x²-49)
= x⁴-28x²+196=30x²-245 | +245
= x⁴-28x²+441=30x² | -30x²
= x⁴-58x²+441=0

x⁴=a² x²=a -> a²-58a+441=0

a1|a2 = 58/2 ± √(58/2)²-441
a1|a2 = 58/2 ± √3364/4-1764/4
a1|a2 = 58/2 ± √1600/4
a1|a2 = 58/2 ± √400
a1|a2 = 58/2 ± 20
a1|a2 = 29 ± 20
a1 = 49
a2 = 9
a= x² -> x1 = ± √49 ; x2= ± √9

You didn't do anything wrong, you got it right. I think I can guess your confusion. It's easy to mess up when substituting the answer back into the original equation and get all the x, x^2, and other things squared mixed up.

x = +-3 or +-7

x = +-3

((+-3)^2 - 14)^2 =
(9 - 14)^2 =
(-5)^2 =
25

5(6(+-3)^2 - 49) =
5(6 * 9 - 49) =
5(54 - 49) =
5 * 5 =
25

+-7

((+-7)^2 - 14)^2 =
(49^2 - 14)^2 =
(2401 - 14)^2 =
2387^2 =
5697769

Oops wait that doesn't seem right. Just to show you the kind of mistakes I kept making.

((+-7)^2 - 14)^2 =
(49 - 14)^2 =
35^2 =
1225

5(6(+-7)^2 - 49) =
5(6 * 49 - 49) =
5(294 - 49) =
5 * 245 =
1225