$x-1$^2 + 16 = $x+2$^2
Expanding both sides:

x^2 - 2x + 1 + 16 = x^2 + 4x + 4
Combine like terms:

x^2 - 2x + 17 = x^2 +4x + 4

Subtract x^2 from both sides:

-2x + 17 = 4x + 4

Subtract 4x from both sides:

-6x + 17 = 4

Subtract 17 from both sides:

-6x = -13

Divide by -6:

x = 13/6

Therefore, x = 13/6.