a² - b² = (a - b)(a + b)

(5x - 1)² - 16x² = 0

(5x - 1)² - (4x)² = 0

(5x - 1 - 4x)(5x - 1 + 4x) = 0

(x - 1)(9x - 1) = 0

x = 1

x = 1/9

Verified answer

(5x-1)²-16x²=0

25x²+1-10x-16x²=0

9x²-10x+1=0

D=100-4×9×1=64=8²

x₁=(10+8)/(9×2)=1

x₂=(10-8)/(9×2)=1/9